M. J. Ablowitz, D. Bar-yaacov, and A. S. Fokas, On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation, Studies in Applied Mathematics, vol.1, issue.2, pp.135-143, 1983.
DOI : 10.1002/sapm1983692135

L. V. Ahlfors, Lectures On Quasiconformal Mappings, 1966.
DOI : 10.1090/ulect/038

P. Albin, C. Guillarmou, L. Tzou, and G. Uhlmann, Inverse Boundary Problems for Systems in Two Dimensions, Annales Henri Poincar??, vol.43, issue.5, pp.e-print, 2011.
DOI : 10.1007/s00023-012-0229-1

URL : https://hal.archives-ouvertes.fr/hal-00595141

G. Alessandrini, Stable determination of conductivity by boundary measurements, Applicable Analysis, vol.1975, issue.1-3, pp.153-172, 1988.
DOI : 10.2307/1971291

G. Alessandrini, Singular solutions of elliptic equations and the determination of conductivity by boundary measurements, Journal of Differential Equations, vol.84, issue.2, pp.252-272, 1990.
DOI : 10.1016/0022-0396(90)90078-4

G. Alessandrini, Open issues of stability for the inverse conductivity problem, Journal of Inverse and Ill-posed Problems, vol.15, issue.5, pp.451-460, 2007.
DOI : 10.1515/jiip.2007.025

G. Alessandrini and E. Rosset, The inverse conductivity problem with one measurement: bounds on the size of the unknown object, SIAM J. Appl. Math, vol.58, issue.4, pp.1060-1071, 1998.

G. Alessandrini and S. Vessella, Lipschitz stability for the inverse conductivity problem, Advances in Applied Mathematics, vol.35, issue.2, pp.207-241, 2005.
DOI : 10.1016/j.aam.2004.12.002

K. Astala and L. Päivärinta, Calder??n???s inverse conductivity problem in the plane, Annals of Mathematics, vol.163, issue.1, pp.265-299, 2006.
DOI : 10.4007/annals.2006.163.265

K. Astala, M. Lassas, and L. Päivärinta, Calder??ns' Inverse Problem for Anisotropic Conductivity in the Plane, Communications in Partial Differential Equations, vol.3, issue.1-2, pp.207-224, 2005.
DOI : 10.2307/1971291

K. Astala, M. Lassas, and L. Päivärinta, The borderlines of invisibility and visibility in Calder??n???s inverse problem, Analysis & PDE, vol.9, issue.1, pp.e-print, 2011.
DOI : 10.2140/apde.2016.9.43

L. Baratchart, J. Leblond, S. Rigat, and E. Russ, Hardy spaces of the conjugate Beltrami equation, Journal of Functional Analysis, vol.259, issue.2, pp.384-427, 2010.
DOI : 10.1016/j.jfa.2010.04.004

URL : https://hal.archives-ouvertes.fr/hal-00401712

L. Baratchart, Y. Fischer, and J. Leblond, Dirichlet/Neumann problems and Hardy classes for the planar conductivity equation, Complex Variables and Elliptic Equations, vol.40, issue.4, pp.e-print, 2011.
DOI : 10.1007/978-3-642-65513-5

URL : https://hal.archives-ouvertes.fr/hal-00909577

J. A. Barceló, T. Barceló, and A. Ruiz, Stability of the Inverse Conductivity Problem in the Plane for Less Regular Conductivities, Journal of Differential Equations, vol.173, issue.2, pp.231-270, 2001.
DOI : 10.1006/jdeq.2000.3920

T. Barceló, D. Faraco, and A. Ruiz, Stability of Calder??n inverse conductivity problem in the plane, Journal de Math??matiques Pures et Appliqu??es, vol.88, issue.6, pp.522-556, 2007.
DOI : 10.1016/j.matpur.2007.07.006

R. Beals and R. R. Coifman, Multidimensional inverse scatterings and nonlinear partial differential equations, Pseudodifferential operators and applications, Proc. Sympos. Pure Math, pp.45-70, 1984.

L. Beilina and M. V. Klibanov, Approximate global convergence and adaptivity for coefficient inverse problems, pp.2012-407
DOI : 10.1007/978-1-4419-7805-9

M. I. Belishev, The Calderón problem for two dimensional manifolds by the BC-method SIAM, J. Math. Anal, vol.35, issue.1, pp.172-182, 2003.

C. Guillarmou and L. Tzou, Calderon inverse Problem with partial data on Riemann Surfaces, Duke Math, J, vol.158, issue.1, pp.83-120, 2011.

C. Guillarmou and L. Tzou, Survey on Calderon inverse problem in dimension 2, Inside Out II, 2011.

C. Guillarmou and L. Tzou, Identification of a connection from Cauchy data space on a Riemann surface with boundary, pp.393-418

B. Gutarts, The inverse boundary problem for the two-dimensional elliptic equation in anisotropic media, J. Math. Stat. Allied Fields, vol.1, 2007.

B. Haberman and D. Tataru, Uniqueness in Calderon's problem with Lipschitz conductivities, 2011, e-print arXiv, pp.1108-6068

H. Haddar and R. Kress, Conformal mapping and impedance tomography, Inverse Problems, vol.26, issue.7, p.74002, 2010.
DOI : 10.1088/0266-5611/26/7/074002

URL : https://hal.archives-ouvertes.fr/hal-00739325

G. M. Henkin and V. Michel, On the Explicit Reconstruction of a Riemann surface from its Dirichlet???Neumann operator, GAFA Geometric And Functional Analysis, vol.17, issue.1, pp.116-155, 2007.
DOI : 10.1007/s00039-006-0590-7

URL : https://hal.archives-ouvertes.fr/hal-00004910

G. M. Henkin and R. G. Novikov, The ¯ ?-equation in the multidimensional inverse scattering problem, Russian Mathematical Surveys, vol.42, issue.3, pp.109-180, 1987.

G. M. Henkin and R. G. Novikov, On the Reconstruction of Conductivity of a Bordered Two-dimensional Surface in ???3 from Electrical Current Measurements on Its Boundary, Journal of Geometric Analysis, vol.9, issue.2, pp.543-587, 2011.
DOI : 10.1007/s12220-010-9158-8

G. M. Henkin and M. Santacesaria, On an inverse problem for anisotropic conductivity in the plane, Inverse Problems, vol.26, issue.9, p.95011, 2010.
DOI : 10.1088/0266-5611/26/9/095011

G. M. Henkin and M. Santacesaria, Gel???fand???Calder??n???s Inverse Problem for Anisotropic Conductivities on Bordered Surfaces in ???3, International Mathematics Research Notices, vol.2012, issue.4, pp.781-809, 2012.
DOI : 10.1093/imrn/rnr046

W. V. Hodge, The theory and applications of harmonic integrals, 1941.

M. I. Isaev, Exponential instability in the Gel'fand inverse problem on the energy intervals, J. Inverse Ill-Posed Probl, pp.453-472, 2011.

M. I. Isaev, Instability in the Gel'fand inverse problem at high energies, 2012, e-print arXiv, pp.1206-2328

M. I. Isaev and R. G. Novikov, Stability estimates for determination of potential from the impedance boundary map, pp.e-print, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00652562

M. I. Isaev and R. G. Novikov, Reconstruction of a potential from the impedance boundary map, 2012, e-print arXiv, pp.1204-0076

M. I. Isaev and R. G. Novikov, Energy and regularity dependent stability estimates for the Gel'fand inverse problem in multidimensions, Journal of Inverse and Ill-Posed Problems, vol.20, issue.3, p.689636
DOI : 10.1515/jip-2012-0024

URL : https://hal.archives-ouvertes.fr/hal-00689636

V. Isakov, Increasing stability for the Schrödinger potential from the Dirichlet-to-Neumann map, Discrete Contin, Dyn. Syst. Ser. S, vol.4, issue.3, pp.631-640, 2011.

R. Kohn and M. Vogelius, Determining conductivity by boundary measurements, Communications on Pure and Applied Mathematics, vol.16, issue.3, pp.289-298, 1984.
DOI : 10.1002/cpa.3160370302

R. Kohn and M. Vogelius, Determining conductivity by boundary measurements II. Interior results, Communications on Pure and Applied Mathematics, vol.56, issue.5, pp.643-667, 1985.
DOI : 10.1002/cpa.3160380513

M. Lassas and G. Uhlmann, On determining a Riemannian manifold from the Dirichlet-to-Neumann map, Annales Scientifiques de l'??cole Normale Sup??rieure, vol.34, issue.5, pp.771-787, 2001.
DOI : 10.1016/S0012-9593(01)01076-X

R. G. Novikov and M. Santacesaria, Monochromatic Reconstruction Algorithms for Two-dimensional Multi-channel Inverse Problems, International Mathematics Research Notices, 2012.
DOI : 10.1093/imrn/rns025

URL : https://hal.archives-ouvertes.fr/hal-00594674

L. Rondi, S. Alessandrini, and . Vessella, A remark on a paper by Alessandrini and Vessella, Advances in Applied Mathematics, vol.36, issue.1, pp.67-69, 2006.
DOI : 10.1016/j.aam.2004.12.003

M. Santacesaria, Global stability for the multi-channel Gel'fand?Calderón inverse problem in two dimensions, Bull. Sci. Math, 2012.

M. Santacesaria, New global stability estimates for the Calder??n problem in two dimensions, Journal of the Institute of Mathematics of Jussieu, vol.22, issue.03, pp.10-1017, 2012.
DOI : 10.1088/0266-5611/21/1/016

M. Santacesaria, Stability estimates for an inverse problem for the Schrödinger equation at negative energy in two dimensions, Appl. Anal, 2012.

J. Sylvester, An anisotropic inverse boundary value problem, Communications on Pure and Applied Mathematics, vol.41, issue.2, pp.201-233, 1990.
DOI : 10.1002/cpa.3160430203

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.484.9273

J. Sylvester and G. Uhlmann, A Global Uniqueness Theorem for an Inverse Boundary Value Problem, The Annals of Mathematics, vol.125, issue.1, pp.153-169, 1987.
DOI : 10.2307/1971291

J. Sylvester and G. Uhlmann, Inverse boundary value problems at the boundary???continuous dependence, Communications on Pure and Applied Mathematics, vol.125, issue.2, pp.197-219, 1988.
DOI : 10.1002/cpa.3160410205

I. N. Vekua, Generalized Analytic Functions, 1962.

L. V. Ahlfors, Lectures On Quasiconformal Mappings, 1966.
DOI : 10.1090/ulect/038

K. Astala, M. Lassas, and L. Päivärinta, Calder??ns' Inverse Problem for Anisotropic Conductivity in the Plane, Communications in Partial Differential Equations, vol.3, issue.1-2, pp.207-224, 2005.
DOI : 10.2307/1971291

D. C. Barber and B. H. Brown, Applied potential tomography, Journal of Physics E: Scientific Instruments, vol.17, issue.9, pp.723-733, 1984.
DOI : 10.1088/0022-3735/17/9/002

R. Beals and R. Coifman, The spectral problem for the Davey-Stewartson and Ishimori hierarchiesNonlinear Evolution Equations : Integrability and Spectral Methodes, Proc. Workshop, pp.15-23, 1988.

A. P. Calderón, On an inverse boundary problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, pp.61-73, 1980.

V. Druskin, The unique solution of the inverse problem in electrical surveying and electrical well logging for piecewise-constant conductivity, Physics of the Solid Earth, vol.18, pp.51-53, 1982.

L. D. Faddeev, Growing solutions of the Schrödinger equation, Dokl. Akad. Nauk SSSR, vol.165, issue.3, pp.514-517, 1965.

L. D. Faddeev, The inverse problem in the quantum theory of scattering. II, Current Problems in Mathematics, Akad. Nauk SSSR, Vsesoyuznyi Inst. Nauchnoi i Tekhnicheskoi Informatsii, pp.93-180, 1974.

A. Friedman and M. Vogelius, Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence, Archive for Rational Mechanics and Analysis, vol.34, issue.4, pp.299-326, 1989.
DOI : 10.1007/BF00281494

I. M. Gel-'fand, Some problems of functional analysis and algebra, Proc. Int. Congr. Math, pp.253-276, 1954.

B. Gutarts, The inverse boundary problem for the two-dimensional elliptic equation in anisotropic media, J. Math. Stat. Allied Fields, vol.1, 2007.

R. Kohn and M. Vogelius, Determining conductivity by boundary measurements II. Interior results, Communications on Pure and Applied Mathematics, vol.56, issue.5, pp.643-667, 1985.
DOI : 10.1002/cpa.3160380513

V. Kolehmainen, M. Lassas, and P. Ola, The Inverse Conductivity Problem with an Imperfectly Known Boundary, SIAM Journal on Applied Mathematics, vol.66, issue.2, pp.365-383, 2005.
DOI : 10.1137/040612737

V. Kolehmainen, M. Lassas, and P. Ola, Calder??n's Inverse Problem with an Imperfectly Known Boundary and Reconstruction Up to a Conformal Deformation, SIAM Journal on Mathematical Analysis, vol.42, issue.3, pp.1371-1381, 2010.
DOI : 10.1137/080716918

A. Nachman, Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem, The Annals of Mathematics, vol.143, issue.1, pp.71-96, 1996.
DOI : 10.2307/2118653

R. Novikov, Multidimensional inverse spectral problem for the equation ??? + (v(x) ? Eu(x))? = 0, Functional Analysis and Its Applications, vol.38, issue.3, pp.263-272, 1988.
DOI : 10.1007/BF01077418

L. Slichter, An Inverse Boundary Value Problem in Electrodynamics, Physics, vol.4, issue.12, pp.411-418, 1933.
DOI : 10.1063/1.1745154

J. Sylvester, An anisotropic inverse boundary value problem, Communications on Pure and Applied Mathematics, vol.41, issue.2, pp.201-233, 1990.
DOI : 10.1002/cpa.3160430203

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.484.9273

I. N. Vekua, Generalized Analytic Functions, 1962.

L. V. Ahlfors, Lectures On Quasiconformal Mappings, 1966.
DOI : 10.1090/ulect/038

K. Astala, M. Lassas, and L. Päivärinta, Calder??ns' Inverse Problem for Anisotropic Conductivity in the Plane, Communications in Partial Differential Equations, vol.3, issue.1-2, pp.207-224, 2005.
DOI : 10.2307/1971291

M. I. Belishev, The Calderón problem for two dimensional manifolds by the BC-method SIAM, J. Math. Anal, vol.35, issue.1, pp.172-182, 2003.

J. Bergh and J. Löfström, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften, 1976.

A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl, pp.19-33, 2008.

A. P. Calderón, On an inverse boundary problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, pp.61-73, 1980.

G. Eskin, Boundary value problem for elliptic pseudodifferential equations, 1981.

L. D. Faddeev, Growing solutions of the Schrödinger equation, Dokl. Akad. Nauk SSSR, vol.165, issue.3, pp.514-517, 1965.

T. W. Gamelin, Complex analysis, Undergraduate Texts in Mathematics, 2001.

A. M. Garsia, On the conformal types of algebraic surfaces of euclidean space, Commentarii Mathematici Helvetici, vol.37, issue.1, pp.49-60, 1962.
DOI : 10.1007/BF02566961

C. F. Gauß, Allgemeine Auflösung der Aufgabe: Die Theile einer gegebenen Fläche auf einer andern so abzubilden, dass die Abbildung dem Abgebildeten in den kleinsten Theilen ähnlich wird, 1825.

I. M. Gel-'fand, Some problems of functional analysis and algebra, Proc. Int. Congr. Math, pp.253-276, 1954.

C. Guillarmou and L. Tzou, Calderon inverse Problem with partial data on Riemann Surfaces, e-print arXiv, pp.908-1417

C. Guillarmou and L. Guillopé, The Determinant of the Dirichlet-to-Neumann Map for Surfaces with Boundary, International Mathematics Research Notices, vol.22, issue.26, p.pp, 2007.
DOI : 10.1093/imrn/rnm099

URL : https://hal.archives-ouvertes.fr/hal-00126393

B. Gutarts, The inverse boundary problem for the two-dimensional elliptic equation in anisotropic media, J. Math. Stat. Allied Fields, vol.1, 2007.

R. Hartshorne, Algebraic geometry, 1977.
DOI : 10.1007/978-1-4757-3849-0

R. Harvey and B. Shiffman, A Characterization of Holomorphic Chains, The Annals of Mathematics, vol.99, issue.3, pp.553-587, 1974.
DOI : 10.2307/1971062

G. Henkin and V. Michel, On the Explicit Reconstruction of a Riemann surface from its Dirichlet???Neumann operator, GAFA Geometric And Functional Analysis, vol.17, issue.1, pp.116-155, 2007.
DOI : 10.1007/s00039-006-0590-7

URL : https://hal.archives-ouvertes.fr/hal-00004910

G. Henkin and R. Novikov, On the reconstruction of conductivity of a bordered twodimensional surface in R 3 from electrical current measurements on its boundary, J. Geom. Anal, vol.21, 2011.

G. Henkin and M. Santacesaria, On an inverse problem for anisotropic conductivity in the plane, Inverse Problems, vol.26, issue.9, p.95011, 2010.
DOI : 10.1088/0266-5611/26/9/095011

W. V. Hodge, The theory and applications of harmonic integrals, 1941.

R. Kohn and M. Vogelius, Determining conductivity by boundary measurements, Communications on Pure and Applied Mathematics, vol.16, issue.3, pp.289-298, 1984.
DOI : 10.1002/cpa.3160370302

R. Kohn and M. Vogelius, Determining conductivity by boundary measurements II. Interior results, Communications on Pure and Applied Mathematics, vol.56, issue.5, pp.643-667, 1985.
DOI : 10.1002/cpa.3160380513

M. Lassas and G. Uhlmann, On determining a Riemannian manifold from the Dirichlet-to-Neumann map, Annales Scientifiques de l'??cole Normale Sup??rieure, vol.34, issue.5, pp.771-787, 2001.
DOI : 10.1016/S0012-9593(01)01076-X

A. Nachman, Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem, The Annals of Mathematics, vol.143, issue.1, pp.71-96, 1996.
DOI : 10.2307/2118653

R. G. Novikov, Multidimensional inverse spectral problem for the equation ??? + (v(x) ? Eu(x))? = 0, Functional Analysis and Its Applications, vol.38, issue.3, pp.263-272, 1988.
DOI : 10.1007/BF01077418

R. A. Rüedy, Embeddings of open riemann surfaces, Commentarii Mathematici Helvetici, vol.46, issue.1, pp.214-225, 1971.
DOI : 10.1007/BF02566840

J. Sylvester, An anisotropic inverse boundary value problem, Communications on Pure and Applied Mathematics, vol.41, issue.2, pp.201-233, 1990.
DOI : 10.1002/cpa.3160430203

I. N. Vekua, Generalized Analytic Functions, 1962.

G. Alessandrini, Stable determination of conductivity by boundary measurements, Applicable Analysis, vol.1975, issue.1-3, pp.153-172, 1988.
DOI : 10.2307/1971291

A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl, pp.19-33, 2008.

A. P. Calderón, On an inverse boundary problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, pp.61-73, 1980.

I. M. Gel-'fand, Some problems of functional analysis and algebra, Proc. Int. Congr. Math, pp.253-276, 1954.

L. Hörmander, The Analysis of Linear Partial Differential Operators I, 1983.

L. Liu, Stability Estimates for the Two-Dimensional Inverse Conductivity Problem, 1997.

N. Mandache, Exponential instability in an inverse problem for the Schr??dinger equation, Inverse Problems, vol.17, issue.5, pp.1435-1444, 2001.
DOI : 10.1088/0266-5611/17/5/313

A. Nachman, Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem, The Annals of Mathematics, vol.143, issue.1, pp.71-96, 1996.
DOI : 10.2307/2118653

R. Novikov, Multidimensional inverse spectral problem for the equation ??? + (v(x) ?

R. Novikov, New global stability estimates for the Gel'fand-Calderon inverse problem, e-print arXiv

J. Sylvester and G. Uhlmann, A Global Uniqueness Theorem for an Inverse Boundary Value Problem, The Annals of Mathematics, vol.125, issue.1, pp.153-169, 1987.
DOI : 10.2307/1971291

I. N. Vekua, Generalized Analytic Functions, 1962.

G. Alessandrini, Stable determination of conductivity by boundary measurements, Applicable Analysis, vol.1975, issue.1-3, pp.153-172, 1988.
DOI : 10.2307/1971291

S. V. Baykov, V. A. Burov, and S. N. Sergeev, Mode Tomography of Moving Ocean, Proc. of the 3rd European Conference on Underwater Acoustics, pp.845-850, 1996.

R. Beals and R. R. Coifman, Multidimensional inverse scatterings and nonlinear partial differential equations, Pseudodifferential operators and applications, Proc. Sympos. Pure Math, pp.45-70, 1984.
DOI : 10.1090/pspum/043/812283

A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl, pp.19-33, 2008.

A. P. Calderón, On an inverse boundary value problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, pp.61-73, 1980.

L. C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol.19, 1998.

L. D. Faddeev, Growing solutions of the Schrödinger equation, Dokl. Akad. Nauk SSSR, vol.165, issue.3, pp.514-517, 1965.

I. M. Gel-'fand, Some aspects of functional analysis and algebra, Proceedings of the International Congress of Mathematicians, pp.253-276, 1954.

M. Isaev, Exponential instability in the Gel'fand inverse problem on the energy intervals, Journal of Inverse and Ill-posed Problems, vol.19, issue.3, pp.453-472, 2011.
DOI : 10.1515/jiip.2011.039

URL : https://hal.archives-ouvertes.fr/hal-00545051

N. Mandache, Exponential instability in an inverse problem for the Schr??dinger equation, Inverse Problems, vol.17, issue.5, pp.1435-1444, 2001.
DOI : 10.1088/0266-5611/17/5/313

R. G. Novikov, Multidimensional inverse spectral problem for the equation ??? + (v(x) ? Eu(x))? = 0, Funkt. Anal. i Pril, pp.11-22, 1988.

R. G. Novikov, New global stability estimates for the Gel'fand???Calderon inverse problem, Inverse Problems, vol.27, issue.1, 2011.
DOI : 10.1088/0266-5611/27/1/015001

URL : https://hal.archives-ouvertes.fr/hal-00451821

R. G. Novikov and M. Santacesaria, A global stability estimate for the Gel'fand-Calderón inverse problem in two dimensions, J. Inverse Ill-Posed Probl, pp.765-785, 2010.

R. G. Novikov and M. Santacesaria, Global uniqueness and reconstruction for the multi-channel Gel??fand???Calder??n inverse problem in two dimensions, Bulletin des Sciences Math??matiques, vol.135, issue.5, pp.421-434, 2011.
DOI : 10.1016/j.bulsci.2011.04.007

L. Xiaosheng, Inverse scattering problem for the Schrödinger operator with external Yang- Mills potentials in two dimensions at fixed energy, Comm. Part. Diff. Eq, vol.30, pp.4-6, 2005.

Z. S. Agranovich and V. A. Marchenko, The inverse problem of scattering theory, Translated from the Russian by B. D. Seckler Gordon and Breach Science Publishers, 1963.

G. Alessandrini, Stable determination of conductivity by boundary measurements, Applicable Analysis, vol.1975, issue.1-3, pp.153-172, 1988.
DOI : 10.2307/1971291

S. V. Baykov, V. A. Burov, and S. N. Sergeev, Mode Tomography of Moving Ocean, Proc. of the 3rd European Conference on Underwater Acoustics, pp.845-850, 1996.

R. Beals and R. R. Coifman, Multidimensional inverse scatterings and nonlinear partial differential equations, Pseudodifferential operators and applications, Proc. Sympos. Pure Math, pp.45-70, 1984.
DOI : 10.1090/pspum/043/812283

J. Bikowski, K. Knudsen, and J. L. Mueller, Direct numerical reconstruction of conductivities in three dimensions using scattering transforms, Inv, 2011.

A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl, pp.19-33, 2008.

V. A. Burov, O. D. Rumyantseva, and T. V. Suchkova, Practical application possibilities of the functional approach to solving inverse scattering problems, Russian) Moscow Phys. Soc. 3, pp.275-278, 1990.

A. P. Calderón, On an inverse boundary problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, pp.61-73, 1980.

B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, The Schrödinger equation in a periodic field and Riemann surfaces, Dokl. Akad. Nauk SSSR, vol.229, issue.1, pp.15-18, 1976.

L. D. Faddeev, Growing solutions of the Schrödinger equation, Dokl. Akad. Nauk SSSR, vol.165, issue.3, pp.514-517, 1965.

I. M. Gel-'fand, Some problems of functional analysis and algebra, Proc. Int. Congr. Math, pp.253-276, 1954.

P. G. Grinevich, The scattering transform for the two-dimensional Schrödinger operator with a potential that decreases at infinity at fixed nonzero energy, Russian) Uspekhi Mat. Nauk 55, pp.3-70, 2000.

R. G. Novikov, Multidimensional inverse spectral problem for the equation ??? + (v(x) ? Eu(x))? = 0, Funkt. Anal. i Pril, pp.11-22, 1988.

R. G. Novikov, The inverse scattering problem on a fixed energy level for the two-dimensional Schr??dinger operator, Journal of Functional Analysis, vol.103, issue.2, pp.409-463, 1992.
DOI : 10.1016/0022-1236(92)90127-5

R. G. Novikov, Formulae and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential, Inverse Problems, vol.21, issue.1, pp.257-270, 2005.
DOI : 10.1088/0266-5611/21/1/016

R. G. Novikov, New global stability estimates for the Gel'fand-Calderon inverse problem, Inv, 2011.

R. G. Novikov and M. Santacesaria, A global stability estimate for the Gel'fand-Calderón inverse problem in two dimensions, J. Inverse Ill-Posed Probl, pp.765-785, 2010.

I. N. Vekua, Generalized Analytic Functions, 1962.

L. Xiaosheng, Inverse scattering problem for the Schrödinger operator with external Yang-Mills potentials in two dimensions at fixed energy, Comm. Part. Diff. Eq, vol.30, pp.4-6, 2005.

B. N. Zakhariev and A. A. Suzko, Direct and inverse problems. Potentials in quantum scattering, Translated from the Russian by G. Pontecorvo, 1990.

Z. S. Agranovich and V. A. Marchenko, The inverse problem of scattering theory, Translated from the Russian by B. D. Seckler Gordon and Breach Science Publishers, 1963.

S. V. Baykov, V. A. Burov, and S. N. Sergeev, Mode Tomography of Moving Ocean, Proc. of the 3rd European Conference on Underwater Acoustics, pp.845-850, 1996.

R. Beals and R. R. Coifman, Multidimensional inverse scatterings and nonlinear partial differential equations, Pseudodifferential operators and applications, Proc. Sympos. Pure Math, pp.45-70, 1984.
DOI : 10.1090/pspum/043/812283

A. V. Bogatyrev, V. A. Burov, S. A. Morozov, O. D. Rumyantseva, and E. G. Sukhov, Numerical Realization of Algorithm for Exact Solution of Two-Dimensional Monochromatic inverse Problem of Acoustical Scattering, Acoust. Imaging, vol.25, pp.65-70, 2000.
DOI : 10.1007/0-306-47107-8_8

A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl, pp.19-33, 2008.

V. A. Burov, N. V. Alekseenko, and O. D. Rumyantseva, Multifrequency generalization of the Novikov algorithm for the two-dimensional inverse scattering problem, Acoustical Physics, vol.55, issue.6, pp.843-856, 2009.
DOI : 10.1134/S1063771009060190

B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, The Schrödinger equation in a periodic field and Riemann surfaces, Dokl. Akad. Nauk SSSR, vol.229, issue.1, pp.15-18, 1976.

L. D. Faddeev, Growing solutions of the Schrödinger equation, Dokl. Akad. Nauk SSSR, vol.165, issue.3, pp.514-517, 1965.

L. D. Faddeev, The inverse problem in the quantum theory of scattering. II, Journal of Mathematical Sciences, vol.5, issue.3, pp.334-396, 1976.

I. M. Gel-'fand, Some problems of functional analysis and algebra, Proc. Int. Congr. Math, pp.253-276, 1954.

P. G. Grinevich, The scattering transform for the two-dimensional Schrödinger operator with a potential that decreases at infinity at fixed nonzero energy, Russian) Uspekhi Mat. Nauk 55, pp.3-70, 2000.

P. G. Grinevich and R. G. Novikov, Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials, Communications in Mathematical Physics, vol.7, issue.1,2, pp.409-446, 1995.
DOI : 10.1007/BF02099609

G. M. Henkin and R. G. Novikov, The ¯ ?-equation in the multidimensional inverse scattering problem, Russian Mathematical Surveys, vol.42, issue.3, pp.109-180, 1987.

M. V. Klibanov, Uniqueness of an inverse problem with single measurement data generated by a plane wave in partial finite differences, Inverse Problems, vol.27, issue.11, p.115005, 2011.
DOI : 10.1088/0266-5611/27/11/115005

S. V. Manakov, The inverse scattering transform for the time-dependent Schrodinger equation and Kadomtsev-Petviashvili equation, Physica D: Nonlinear Phenomena, vol.3, issue.1-2, pp.420-427, 1981.
DOI : 10.1016/0167-2789(81)90145-7

R. G. Novikov, Multidimensional inverse spectral problem for the equation ??? + (v(x) ? Eu(x))? = 0, Funkt. Anal. i Pril, pp.11-22, 1988.

R. G. Novikov, The inverse scattering problem on a fixed energy level for the two-dimensional Schr??dinger operator, Journal of Functional Analysis, vol.103, issue.2, pp.409-463, 1992.
DOI : 10.1016/0022-1236(92)90127-5

R. G. Novikov, Rapidly converging approximation in inverse quantum scattering in dimension 2, Physics Letters A, vol.238, issue.2-3, pp.73-78, 1998.
DOI : 10.1016/S0375-9601(97)00713-5

R. G. Novikov, Approximate solution of the inverse problem of quantum scattering theory with fixed energy in dimension 2, Proc. Steklov Inst. Math. 225, pp.301-318, 1999.

R. G. Novikov, Formulae and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential, Inverse Problems, vol.21, issue.1, pp.257-270, 2005.
DOI : 10.1088/0266-5611/21/1/016

R. G. Novikov, The ¯ ? approach to approximate inverse scattering at fixed energy in three dimensions, Int. Math. Res. Papers, issue.6, pp.287-349, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00004900

R. G. Novikov and M. Santacesaria, A global stability estimate for the Gel'fand-Calderón inverse problem in two dimensions, J. Inverse Ill-Posed Probl, pp.765-785, 2010.

R. G. Novikov and M. Santacesaria, Global uniqueness and reconstruction for the multi-channel Gel??fand???Calder??n inverse problem in two dimensions, Bulletin des Sciences Math??matiques, vol.135, issue.5, pp.421-434, 2011.
DOI : 10.1016/j.bulsci.2011.04.007

M. Santacesaria, Global stability for the multi-channel Gel'fand-Calderón inverse problem in two dimensions, e-print arXiv, pp.1102-5175

L. Xiaosheng, Inverse scattering problem for the Schrödinger operator with external Yang-Mills potentials in two dimensions at fixed energy, Comm. Part. Diff. Eq, vol.30, pp.4-6, 2005.

B. N. Zakhariev and A. A. Suzko, Direct and inverse problems. Potentials in quantum scattering, Translated from the Russian by G. Pontecorvo, 1990.

G. Alessandrini, Stable determination of conductivity by boundary measurements, Applicable Analysis, vol.1975, issue.1-3, pp.153-172, 1988.
DOI : 10.2307/1971291

G. Alessandrini and S. Vessella, Lipschitz stability for the inverse conductivity problem, Advances in Applied Mathematics, vol.35, issue.2, pp.207-241, 2005.
DOI : 10.1016/j.aam.2004.12.002

K. Astala and L. Päivärinta, Calder??n???s inverse conductivity problem in the plane, Annals of Mathematics, vol.163, issue.1, pp.265-299, 2006.
DOI : 10.4007/annals.2006.163.265

J. A. Barceló, T. Barceló, and A. Ruiz, Stability of the Inverse Conductivity Problem in the Plane for Less Regular Conductivities, Journal of Differential Equations, vol.173, issue.2, pp.231-270, 2001.
DOI : 10.1006/jdeq.2000.3920

T. Barceló, D. Faraco, and A. Ruiz, Stability of Calder??n inverse conductivity problem in the plane, Journal de Math??matiques Pures et Appliqu??es, vol.88, issue.6, pp.522-556, 2007.
DOI : 10.1016/j.matpur.2007.07.006

R. Beals and R. R. Coifman, Multidimensional inverse scatterings and nonlinear partial differential equations, Pseudodifferential operators and applications, Proc. Sympos. Pure Math, pp.45-70, 1984.
DOI : 10.1090/pspum/043/812283

E. Beretta and E. Francini, Lipschitz Stability for the Electrical Impedance Tomography Problem: The Complex Case, Communications in Partial Differential Equations, vol.17, issue.10, pp.1723-1749, 2011.
DOI : 10.1007/BF01262694

A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl, pp.19-33, 2008.

A. P. Calderón, On an inverse boundary problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, pp.61-73, 1980.

B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, The Schrödinger equation in a periodic field and Riemann surfaces, Dokl. Akad. Nauk SSSR, vol.229, issue.1, pp.15-18, 1976.

L. D. Faddeev, Growing solutions of the Schrödinger equation, Dokl. Akad. Nauk SSSR, vol.165, issue.3, pp.514-517, 1965.

I. M. Gel-'fand, Some aspects of functional analysis and algebra, Proceedings of the International Congress of Mathematicians, pp.253-276, 1954.

P. G. Grinevich and S. P. Novikov, Two-dimensional ?inverse scattering problem? for negative energies and generalized-analytic functions. I. Energies below the ground state, Functional Analysis and Its Applications, vol.42, issue.3, pp.19-27, 1988.
DOI : 10.1007/BF01077719

G. M. Henkin and R. G. Novikov, The ¯ ?-equation in the multidimensional inverse scattering problem, Russian Mathematical Surveys, vol.42, issue.3, pp.109-180, 1987.

M. Isaev, Exponential instability in the Gel'fand inverse problem on the energy intervals, Journal of Inverse and Ill-posed Problems, vol.19, issue.3, pp.453-472, 2011.
DOI : 10.1515/jiip.2011.039

URL : https://hal.archives-ouvertes.fr/hal-00545051

R. Kohn and M. Vogelius, Determining conductivity by boundary measurements, Communications on Pure and Applied Mathematics, vol.16, issue.3, pp.289-298, 1984.
DOI : 10.1002/cpa.3160370302

R. Kohn and M. Vogelius, Determining conductivity by boundary measurements II. Interior results, Communications on Pure and Applied Mathematics, vol.56, issue.5, pp.643-667, 1985.
DOI : 10.1002/cpa.3160380513

L. Liu, Stability Estimates for the Two-Dimensional Inverse Conductivity Problem, 1997.

N. Mandache, Exponential instability in an inverse problem for the Schr??dinger equation, Inverse Problems, vol.17, issue.5, pp.1435-1444, 2001.
DOI : 10.1088/0266-5611/17/5/313

A. Nachman, Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem, The Annals of Mathematics, vol.143, issue.1, pp.71-96, 1996.
DOI : 10.2307/2118653

R. G. Novikov, Multidimensional inverse spectral problem for the equation ??? + (v(x) ? Eu(x))? = 0, Funkt. Anal. i Pril, pp.11-22, 1988.

R. G. Novikov, The inverse scattering problem on a fixed energy level for the two-dimensional Schr??dinger operator, Journal of Functional Analysis, vol.103, issue.2, pp.409-463, 1992.
DOI : 10.1016/0022-1236(92)90127-5

R. G. Novikov, Approximate solution of the inverse problem of quantum scattering theory with fixed energy in dimension 2, Proc. Steklov Inst. Math. 225, pp.301-318, 1999.

R. G. Novikov, Formulae and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential, Inverse Problems, vol.21, issue.1, pp.257-270, 2005.
DOI : 10.1088/0266-5611/21/1/016

R. G. Novikov, New global stability estimates for the Gel'fand???Calderon inverse problem, Inverse Problems, vol.27, issue.1, 2011.
DOI : 10.1088/0266-5611/27/1/015001

URL : https://hal.archives-ouvertes.fr/hal-00451821

R. G. Novikov and N. N. Novikova, On stable determination of potential by boundary measurements, ESAIM: Proc. 26, pp.94-99, 2009.
DOI : 10.1051/proc/2009007

URL : https://hal.archives-ouvertes.fr/hal-00194514

R. G. Novikov and M. Santacesaria, A global stability estimate for the Gel'fand-Calderón inverse problem in two dimensions, J. Inverse Ill-Posed Probl, pp.765-785, 2010.

J. Sylvester and G. Uhlmann, A Global Uniqueness Theorem for an Inverse Boundary Value Problem, The Annals of Mathematics, vol.125, issue.1, pp.153-169, 1987.
DOI : 10.2307/1971291

I. N. Vekua, Generalized Analytic Functions Paper H PAPER H Stability estimates for an inverse problem for the Schrödinger equation at negative energy in two dimensions, 1962.

G. Alessandrini, Stable determination of conductivity by boundary measurements, Applicable Analysis, vol.1975, issue.1-3, pp.153-172, 1988.
DOI : 10.2307/1971291

G. Alessandrini and S. Vessella, Lipschitz stability for the inverse conductivity problem, Advances in Applied Mathematics, vol.35, issue.2, pp.207-241, 2005.
DOI : 10.1016/j.aam.2004.12.002

J. A. Barceló, T. Barceló, and A. Ruiz, Stability of the Inverse Conductivity Problem in the Plane for Less Regular Conductivities, Journal of Differential Equations, vol.173, issue.2, pp.231-270, 2001.
DOI : 10.1006/jdeq.2000.3920

T. Barceló, D. Faraco, and A. Ruiz, Stability of Calder??n inverse conductivity problem in the plane, Journal de Math??matiques Pures et Appliqu??es, vol.88, issue.6, pp.522-556, 2007.
DOI : 10.1016/j.matpur.2007.07.006

L. Beilina and M. V. Klibanov, Approximate global convergence and adaptivity for coefficient inverse problems, pp.2012-407
DOI : 10.1007/978-1-4419-7805-9

A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl, pp.19-33, 2008.

A. P. Calderón, On an inverse boundary problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, pp.61-73, 1980.

V. L. Druskin, The unique solution of the inverse problem in electrical surveying and electrical well logging for piecewise-constant conductivity, Izvestiya, Physics of the Solid Earth, vol.18, issue.1, pp.51-53, 1982.

B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, The Schrödinger equation in a periodic field and Riemann surfaces, Dokl. Akad. Nauk SSSR, vol.229, issue.1, pp.15-18, 1976.

L. D. Faddeev, Growing solutions of the Schrödinger equation, Dokl. Akad. Nauk SSSR, vol.165, issue.3, pp.514-517, 1965.

I. M. Gel-'fand, Some aspects of functional analysis and algebra, Proceedings of the International Congress of Mathematicians, pp.253-276, 1954.

P. G. Grinevich, The scattering transform for the two-dimensional Schrödinger operator with a potential that decreases at infinity at fixed nonzero energy, Russian) Uspekhi Mat. Nauk 55, pp.3-70, 2000.

P. G. Grinevich and S. P. Novikov, Two-dimensional ?inverse scattering problem? for negative energies and generalized-analytic functions. I. Energies below the ground state, Functional Analysis and Its Applications, vol.42, issue.3, pp.19-27, 1988.
DOI : 10.1007/BF01077719

M. I. Isaev, Exponential instability in the Gel'fand inverse problem on the energy intervals, Journal of Inverse and Ill-posed Problems, vol.19, issue.3, pp.453-472, 2011.
DOI : 10.1515/jiip.2011.039

URL : https://hal.archives-ouvertes.fr/hal-00545051

M. I. Isaev and R. G. Novikov, Stability estimates for determination of potential from the impedance boundary map, e-print arXiv, pp.1112-3728

V. Isakov, Increasing stability for the Schrödinger potential from the Dirichlet-to-Neumann map, Discrete Contin, Dyn. Syst. Ser. S, vol.4, issue.3, pp.631-640, 2011.

R. Kohn and M. Vogelius, Determining conductivity by boundary measurements II. Interior results, Communications on Pure and Applied Mathematics, vol.56, issue.5, pp.643-667, 1985.
DOI : 10.1002/cpa.3160380513

M. M. Lavrent-'ev, V. G. Romanov, and S. P. Shishat·ski?-i, Ill-posed problems of mathematical physics and analysis, Translated from the Russian by, J. R. Schulenberger. Translation edited by Lev J. Leifman. Translations of Mathematical Monographs, vol.64, 1986.

L. Liu, Stability Estimates for the Two-Dimensional Inverse Conductivity Problem, 1997.

N. Mandache, Exponential instability in an inverse problem for the Schr??dinger equation, Inverse Problems, vol.17, issue.5, pp.1435-1444, 2001.
DOI : 10.1088/0266-5611/17/5/313

A. Nachman, Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem, The Annals of Mathematics, vol.143, issue.1, pp.71-96, 1996.
DOI : 10.2307/2118653

R. G. Novikov, Multidimensional inverse spectral problem for the equation ??? + (v(x) ? Eu(x))? = 0, Funkt. Anal. i Pril, pp.11-22, 1988.

R. G. Novikov, The inverse scattering problem on a fixed energy level for the two-dimensional Schr??dinger operator, Journal of Functional Analysis, vol.103, issue.2, pp.409-463, 1992.
DOI : 10.1016/0022-1236(92)90127-5

R. G. Novikov, Approximate solution of the inverse problem of quantum scattering theory with fixed energy in dimension 2, Proc. Steklov Inst. Math. 225, pp.301-318, 1999.

R. G. Novikov, Formulae and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential, Inverse Problems, vol.21, issue.1, pp.257-270, 2005.
DOI : 10.1088/0266-5611/21/1/016

R. G. Novikov, The ?-approach to approximate inverse scattering at fixed energy in three dimensions, IMRP Int. Math. Res. Pap, issue.6, pp.287-349, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00004900

R. G. Novikov, New global stability estimates for the Gel'fand???Calderon inverse problem, Inverse Problems, vol.27, issue.1, 2011.
DOI : 10.1088/0266-5611/27/1/015001

URL : https://hal.archives-ouvertes.fr/hal-00451821

R. G. Novikov and M. Santacesaria, A global stability estimate for the Gel'fand-Calderón inverse problem in two dimensions, J. Inverse Ill-Posed Probl, pp.765-785, 2010.

R. G. Novikov and M. Santacesaria, Monochromatic Reconstruction Algorithms for Two-dimensional Multi-channel Inverse Problems, International Mathematics Research Notices, 2012.
DOI : 10.1093/imrn/rns025

URL : https://hal.archives-ouvertes.fr/hal-00594674

L. Rondi, S. Alessandrini, and . Vessella, A remark on a paper by Alessandrini and Vessella, Advances in Applied Mathematics, vol.36, issue.1, pp.67-69, 2006.
DOI : 10.1016/j.aam.2004.12.003

M. Santacesaria, New global stability estimates for the Calder??n problem in two dimensions, Journal of the Institute of Mathematics of Jussieu, vol.22, issue.03, pp.10-1017, 2012.
DOI : 10.1088/0266-5611/21/1/016

J. Sylvester and G. Uhlmann, A Global Uniqueness Theorem for an Inverse Boundary Value Problem, The Annals of Mathematics, vol.125, issue.1, pp.153-169, 1987.
DOI : 10.2307/1971291