). G. Allaire and M. Amar, Boundary layer tails in periodic homogenization, ESAIM: Control, Optimisation and Calculus of Variations, pp.209-243, 1999.

). G. Allaire and A. Piatnitski, UNIFORM SPECTRAL ASYMPTOTICS FOR SINGULARLY PERTURBED LOCALLY PERIODIC OPERATORS, Communications in Partial Differential Equations, vol.90, issue.4, pp.3-4, 2002.
DOI : 10.1081/PDE-120002871

). G. Allaire, Y. Capdeboscq, A. Piatnitski, V. Siess, and M. Vanninathan, Homogenization of Periodic Systems with Large Potentials, Archive for Rational Mechanics and Analysis, vol.90, issue.2, pp.179-220, 2004.
DOI : 10.1007/s00205-004-0332-7

G. Allaire and A. Raphael, Homogenization of a convection???diffusion model with reaction in a porous medium, Comptes Rendus Mathematique, vol.344, issue.8, pp.523-528, 2007.
DOI : 10.1016/j.crma.2007.03.008

). N. Bakhvalov and G. P. Panasenko, Homogenization: Averaging processes in periodic media(Russian); English transl, p.1984, 1989.

). A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structure, Studies in Mathematics and its Applications, 1978.

). A. Braides and A. Defranceschi, Homogenization of multiple integrals, Oxford Lecture Series in Mathematics and its Applications, 1998.

). Y. Capdeboscq, Homogenization of a diffusion equation with drift, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.327, issue.9, pp.807-812, 1998.
DOI : 10.1016/S0764-4442(99)80109-8

). Y. Capdeboscq, Homogenization of a neutronic critical diffusion problem with drift, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.132, issue.03, pp.567-594, 2002.
DOI : 10.1017/S0308210500001785

G. Cardone, A. Esposito, and S. A. Nazarov, Korn's inequality for periodic solids and convergence rate of homogenization (submitted)

). D. Cioranescu and P. Donato, An introduction to homogenization, Oxford Lecture Series in Mathematics and its Applications, 1999.

). D. Cioranescu and J. Saint-jean-paulin, Homogenization of Reticulated Structures, Applied Mechanics Reviews, vol.54, issue.4, 1999.
DOI : 10.1115/1.1383678

P. Donato and A. Piatnitski, Averaging of nonstationary parabolic operators with large lower order terms. Multi Scale Problems and Asymptotic Analysis, GAKUTO Internat. Ser. Math. Sci. Appl, vol.24, pp.153-165, 2005.

). J. Flavin and R. J. Knops, Asymptotic behaviour of solutions to semi-linear elliptic equations on the half-cylinder, ZAMP Zeitschrift f???r angewandte Mathematik und Physik, vol.5, issue.3, pp.43-405, 1992.
DOI : 10.1007/BF00946237

). J. Flavin, R. J. Knops, and L. E. Payne, ASYMPTOTIC AND OTHER ESTIMATES FOR A SEMILINEAR ELLIPTIC EQUATION IN A CYLINDER, The Quarterly Journal of Mechanics and Applied Mathematics, vol.45, issue.4, pp.45-617, 1992.
DOI : 10.1093/qjmam/45.4.617

). S. Kesavan, Homogenization of Elliptic Eigenvalue Problems: Part 1, Appl. Math. Optim, issue.05336175, pp.153-167, 1979.

). S. Kesavan, Homogenization of Elliptic Eigenvalue Problems: Part 2, Appl. Math. Optim, issue.05336175, pp.197-216, 1979.

). R. Knops and L. E. Payne, Asymptotic behaviour of solutions to the equation of constant mean curvature on a three-dimensional region, Meccanica, vol.164, issue.5, pp.31-597, 1996.
DOI : 10.1007/BF00420829

). R. Knops and C. Lupoli, Some recent results on Saint-Venant's principle, Nonlinear analysis and continuum mechanics, pp.61-71, 1998.

S. M. Kozlov, Reducibility of Quasiperiodic Differential Operators and Averaging. Transc, 1984.

M. V. Kozlova, Averaging of a three-dimensional problem in elasticity theory for a thin nonhomogeneous beam. (Russian), Vestnik Moskov, Univ. Ser. I Mat. Mekh. Math. Bull, vol.44, issue.55, pp.6-10, 1989.

). M. Kozlova, Averaging a three-dimensional problem of elasticity theory in a nonhomogeneous rod. (Russian) , Zh, Vychisl. Mat. i Mat. Fiz. Comput. Math. Math. Phys, vol.31, issue.3110, pp.1592-1596, 1991.

). V. Kondratiev and O. A. Oleinik, On asymptotics of solutions of nonlinear second order elliptic equations in cylindrical domains, Partial differential equations and functional analysis, Progr. Nonlinear Differential Equations Appl, vol.22, pp.160-173, 1996.

). E. Landis and G. P. Panasenko, A variant of a theorem of Phragmen-Lindelof type for elliptic equationswith coefficients that are periodic in all variables but one, Trudy Sem, Petrovsk, issue.0549625, pp.105-136, 1979.

V. A. Marchenko and E. Ya, Khruslov, Homogenization of partial differential equations, Progress in Mathematical Physics, 2006.

G. Dal-maso, An introduction to ?-convergence, Progress in Nonlinear Differential Equations and their Applications, 1993.
DOI : 10.1007/978-1-4612-0327-8

). G. Milton, The theory of composites, Cambridge Monographs on Applied and Computational Mathematics, vol.6, 2002.
DOI : 10.1017/CBO9780511613357

). F. Murat and A. Sili, Asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin cylinders, C. R. Acad. Sci. Paris Sér. I Math, pp.328-179, 1999.

S. A. Nazarov, Polynomial property of self-adjoint boundary value problems and algebraical description of their attributes, pp.54-77, 1999.

). S. Nazarov, Structure of the solutions of boundary value problems in thin regions (Russian . English summary), Vestnik Leningrad, Univ. Mat. Mekh. Astronom, vol.126, issue.0664066, pp.65-68, 1982.

). S. Nazarov, Justification of the asymptotic theory of thin rods. Integral and pointwise estimates, Journal of Mathematical Sciences, vol.84, issue.No. 2, pp.4245-4279, 1999.
DOI : 10.1007/BF02365044

S. A. Nazarov, Asymptotics of negative eigenvalues of a Dirichlet problem with sign-changing density function Trudy seminara I.G.Petrovskogo, p.28, 2009.

S. A. Nazarov and A. L. Piatnitski, Homogenization of a spectral Dirichlet problem for a system of differential equation with highly-oscillating coefficients in the case of the sign-changing density, R&D Report, issue.2, 2009.

S. A. Nazarov, I. L. Pankratova, A. L. Piatnitski, and R. Report, Homogenization of spectral problem for periodic elliptic operators with sign-changing weight function, 2008.

G. Duvaut and J. Lions, Inequalities in Mechanics and Physics, 1976.

). J. Flavin and R. J. Knops, Asymptotic behaviour of solutions to semi-linear elliptic equations on the half-cylinder, ZAMP Zeitschrift f???r angewandte Mathematik und Physik, vol.5, issue.3, pp.43-405, 1992.
DOI : 10.1007/BF00946237

). J. Flavin, R. J. Knops, and L. E. Payne, ASYMPTOTIC AND OTHER ESTIMATES FOR A SEMILINEAR ELLIPTIC EQUATION IN A CYLINDER, The Quarterly Journal of Mechanics and Applied Mathematics, vol.45, issue.4, pp.45-617, 1992.
DOI : 10.1093/qjmam/45.4.617

). D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order Reprint of the 1998 edition, Classics in Mathematics, 2001.

). C. Horgan, L. Wheeler, and M. Tureltaub, A Saint-Venant principle for the gradient in the Neumann problem, Z. Angew. Math. Phys, vol.26, issue.0366152, pp.141-153, 1975.

). C. Horgan and L. Wheeler, A two?dimensional Saint?Venant principle for second order linear elliptic equations, Quart. Appl. Math, vol.3477, issue.0450770, pp.257-270, 1976.

). R. Knops and L. E. Payne, Asymptotic behaviour of solutions to the equation of constant mean curvature on a three-dimensional region, Meccanica, vol.164, issue.5, pp.31-597, 1996.
DOI : 10.1007/BF00420829

). R. Knops and C. Lupoli, Some recent results on Saint-Venant's principle, Nonlinear analysis and continuum mechanics, pp.61-71, 1998.

J. K. Knowles, A Saint-Venant principle for a class of second-order elliptic boundary value problems, Zeitschrift f??r angewandte Mathematik und Physik ZAMP, vol.4, issue.4, pp.473-490, 1967.
DOI : 10.1007/BF01601718

V. A. Kondratiev and O. A. Oleinik, On the behaviour at infinity of solutions of elliptic systems with finite energy integral, Arch. Rational Mech. Anal, issue.11, pp.99-75, 1987.

). M. Krasnosel-'skij, E. A. Lifshits, and A. V. Sobolev, Positive Linear Systems: the Method of Positive Operators, Heldermann, 1989.

). V. Kondratiev and O. A. Oleinik, On asymptotics of solutions of nonlinear second order elliptic equations in cylindrical domains, Partial differential equations and functional analysis, Progr. Nonlinear Differential Equations Appl, vol.22, pp.160-173, 1996.

). E. Landis and G. P. Panasenko, A variant of a theorem of Phragmen-Lindelof type for elliptic equationswith coefficients that are periodic in all variables but one, Trudy Sem, pp.105-136, 1979.

). J. Lions, Some Methods in the Mathematical Analysis of Systems and Their Controls, Kexue Chubanshe, issue.0664760, 1981.

S. A. Nazarov, Polynomial property of self-adjoint boundary value problems and algebraical description of their attributes, pp.54-77, 1999.

O. A. Oleinik and G. A. Yosifian, Boundary value problems for second order elliptic equations in unbounded domains and Saint-Venant's principle, pp.4-269, 1977.

). G. Panasenko, Multi-Scale Modelling for Structures and Composites, 2005.

). N. Bakhvalov and G. P. Panasenko, Homogenization: Averaging processes in periodic media(Russian); English transl, p.1984, 1989.

). A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structure, Studies in Mathematics and its Applications, 1978.

). D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition, Classics in Mathematics, 2001.

M. V. Kozlova, Averaging of a three-dimensional problem in elasticity theory for a thin nonhomogeneous beam. (Russian), Vestnik Moskov, Univ. Ser. I Mat. Mekh. Math. Bull, vol.44, issue.55, pp.6-10, 1989.

). M. Kozlova, Averaging a three-dimensional problem of elasticity theory in a nonhomogeneous rod. (Russian) , Zh, Vychisl. Mat. i Mat. Fiz. Comput. Math. Math. Phys, vol.31, issue.3110, pp.1592-1596, 1991.

O. A. Ladyzhenskaya and N. N. , Ural'tseva, Linear and quasilinear elliptic equations, 1968.

). F. Murat and A. Sili, Asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin cylinders, C. R. Acad. Sci. Paris Sér. I Math, pp.328-179, 1999.

). S. Nazarov, Structure of the solutions of boundary value problems in thin regions (Russian . English summary), Vestnik Leningrad, Univ. Mat. Mekh. Astronom, vol.126, issue.0664066, pp.65-68, 1982.

). S. Nazarov, Justification of the asymptotic theory of thin rods. Integral and pointwise estimates, Journal of Mathematical Sciences, vol.84, issue.No. 2, pp.4245-4279, 1999.
DOI : 10.1007/BF02365044

). G. Panasenko, Asymptotic analysis of bar systems. I. (English summary), Russian J. Math. Phys, vol.2, issue.3, pp.325-352, 1994.

). G. Panasenko, Asymptotic analysis of bar systems, II, Russian J. Math. Phys, vol.4, issue.1, pp.87-116, 1996.

). I. Pankratova and A. Piatnitski, On the behaviour at infinity of solutions to stationary convectiondiffusion equation in a cylinder, DCDS-B, vol.11, issue.4, 2009.

). S. Pastukhova, Averaging for nonlinear problems in the theory of elasticity on thin periodic structures, Dokl. Akad. Nauk, pp.383-596, 2002.

). L. Trabucho and J. M. Viaño, Derivation of generalized models for linear elastic beams by asymptotic expansion methods, Applications of multiple scaling in mechanis, Rech. Math. Appl, pp.302-315, 1986.

). Z. Tutek and I. Aganovi´caganovi´c, A justification of the one-dimensional linear model of elastic beam, Mathematical Methods in the Applied Sciences, vol.11, issue.4, pp.502-515, 1986.
DOI : 10.1002/mma.1670080133

). M. Veiga, Asymptotic method applied to a beam with a variable cross section. (English summary) Asymptotic methods for elastic structures, de Gruyter, pp.237-254, 1993.

A. (. Allaire and . Raphael, Homogenization of a convection???diffusion model with reaction in a porous medium, Comptes Rendus Mathematique, vol.344, issue.8, pp.523-528, 2007.
DOI : 10.1016/j.crma.2007.03.008

J. (. Aronson and . Serrin, Local behavior of solutions of quasilinear parabolic equations, Archive for Rational Mechanics and Analysis, vol.113, issue.2, pp.81-122, 1967.
DOI : 10.1007/BF00281291

. (. Aronson, Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa, vol.22, issue.3, pp.607-694, 1968.

G. (. Bakhvalov and . Panasenko, Homogenization: Averaging processes in periodic media, 1989.

J. (. Bensoussan, G. Lions, and . Papanicolaou, Asymptotic Analysis for Periodic Structure, Studies in Mathematics and its Applications, 1978.

A. (. Donato and . Piatnitski, Averaging of nonstationary parabolic operators with large lower order terms. Multi Scale Problems and Asymptotic Analysis, GAKUTO Internat. Ser. Math. Sci. Appl, vol.24, pp.153-165, 2005.

G. (. Kozlova and . Panasenko, Averaging a three-dimensional problem of elasticity theory in a nonhomogeneous rod, Comput. Math. Math. Phys, issue.10, pp.31-128, 1992.

V. (. Ladyzenskaja and N. N. Solonnikov, Ural'ceva, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs, vol.23, 1967.

A. (. Pankratova and . Piatnitski, On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder, Discrete and Continuous Dynamical Systems - Series B, vol.11, issue.4, pp.935-970, 2009.
DOI : 10.3934/dcdsb.2009.11.935

J. (. Trabucho and . Viaño, Derivation of generalized models for linear elastic beams by asymptotic expansion methods, Applications of multiple scaling in mechanis, Rech. Math. Appl, pp.302-315, 1986.

. (. Tutek, A homogenized model of rod in linear elasticity, Applications of multiple scaling in mechanis, Rech. Math. Appl, pp.302-315, 1986.

S. (. Zhikov, O. A. Kozlov, and . Oleinik, Homogenization of differential operators and integral functionals, 1994.

. (. Zhikov, On an extension of the method of two-scale convergence and its applications, Sbornik: Mathematics, vol.191, issue.7, pp.973-1014, 2000.
DOI : 10.1070/SM2000v191n07ABEH000491

). G. Allaire, Y. Capdeboscq, A. Piatnitski, V. Siess, and M. Vanninathan, Homogenization of Periodic Systems with Large Potentials, Archive for Rational Mechanics and Analysis, vol.90, issue.2, pp.179-220, 2004.
DOI : 10.1007/s00205-004-0332-7

G. Allaire, I. Pankratova, and A. Piatnitski, Homogenization of a nonstationary convection-diffusion equation with large convection in a thin rod and in a layer preprint

). G. Allaire and A. Piatnitski, Uniform spectral asymptotics for singularly perturbed locally periodic operators Comm, Partial Differential Equations, vol.27, pp.3-4, 2002.

G. Allaire and A. Raphael, Homogenization of a convection???diffusion model with reaction in a porous medium, Comptes Rendus Mathematique, vol.344, issue.8, pp.523-528, 2007.
DOI : 10.1016/j.crma.2007.03.008

). D. Aronson, Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa, vol.22, issue.04355943, pp.607-694, 1968.

R. Bauelos and K. Burdzy, On the ???Hot Spots??? Conjecture of J. Rauch, Journal of Functional Analysis, vol.164, issue.1, pp.1-33, 1999.
DOI : 10.1006/jfan.1999.3397

). A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structure, Studies in Mathematics and its Applications, 1978.

). A. Bourgeat, M. Jurak, and A. , Averaging a transport equation with small diffusion and oscillating velocity, Mathematical Methods in the Applied Sciences, vol.49, issue.2, pp.95-117, 2003.
DOI : 10.1002/mma.344

K. Burdzy and W. Werner, A counterexample to the " hot spots, conjecture Ann. of Math, issue.2 1, pp.149-309, 1999.

). Y. Capdeboscq, Homogenization of a diffusion equation with drift, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.327, issue.9, pp.807-812, 1998.
DOI : 10.1016/S0764-4442(99)80109-8

Y. Capdeboscq, Homogenization of a neutronic critical diffusion problem with drift, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.132, issue.03, pp.567-594, 2002.
DOI : 10.1017/S0308210500001785

P. Donato and A. Piatnitski, Averaging of nonstationary parabolic operators with large lower order terms. Multi Scale Problems and Asymptotic Analysis, GAKUTO Internat. Ser. Math. Sci. Appl, vol.24, pp.153-165, 2005.

J. Douglas and T. Russell, Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures

). D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order Reprint of the 1998 edition, Classics in Mathematics, 2001.

U. Hornung, Homogenization and Porous Media, Interdiscip. Appl. Math, vol.6, 1997.
DOI : 10.1007/978-1-4612-1920-0

S. M. Kozlov, Reducibility of Quasiperiodic Differential Operators and Averaging. Transc, pp.101-126, 1984.

V. (. Ladyzenskaja and N. N. Solonnikov, Ural'ceva, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs, vol.23, 1967.

). I. Pankratova and A. Piatnitski, On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder, Discrete and Continuous Dynamical Systems - Series B, vol.11, issue.4, 2009.
DOI : 10.3934/dcdsb.2009.11.935

). A. Piatnitski, AVERAGING A SINGULARLY PERTURBED EQUATION WITH RAPIDLY OSCILLATING COEFFICIENTS IN A LAYER, Mathematics of the USSR-Sbornik, vol.49, issue.1, pp.19-40, 1984.
DOI : 10.1070/SM1984v049n01ABEH002694

). O. Pironneau, On the transport-diffusion algorithm and its applications to the Navier-Stokes equations Numer, Math, vol.3882, issue.0654100 3, pp.309-332, 1981.

J. Rauch, Lecture #1. Five problems: An introduction to the qualitative theory of partial differential equations, Tulane Univ. Lecture Notes in Math, vol.446, pp.355-369, 1974.
DOI : 10.1007/BFb0070610

). V. Zhikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of differential operators and integral functionals, 1994.

). V. Zhikov, Asymptotic behavior and stabilization of solutions of a second-order parabolic equation with lowest terms, Transc. Moscow Math. Soc, vol.2, issue.0737901, 1984.

). G. Allaire, Y. Capdeboscq, A. Piatnitski, V. Siess, and M. Vanninathan, Homogenization of Periodic Systems with Large Potentials, Archive for Rational Mechanics and Analysis, vol.90, issue.2, pp.179-220, 2004.
DOI : 10.1007/s00205-004-0332-7

G. Allaire and A. Raphael, Homogenization of a convection???diffusion model with reaction in a porous medium, Comptes Rendus Mathematique, vol.344, issue.8, pp.523-528, 2007.
DOI : 10.1016/j.crma.2007.03.008

G. Allaire, I. Pankratova, and A. Piatnitski, Homogenization and concentration for a diffusion equation with large convection in a bounded domain, Journal of Functional Analysis, vol.262, issue.1
DOI : 10.1016/j.jfa.2011.09.014

URL : https://hal.archives-ouvertes.fr/hal-00784043

). A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structure, Studies in Mathematics and its Applications, 1978.

). Y. Capdeboscq, Homogenization of a diffusion equation with drift, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.327, issue.9, pp.807-812, 1998.
DOI : 10.1016/S0764-4442(99)80109-8

P. Donato and A. Piatnitski, Averaging of nonstationary parabolic operators with large lower order terms. Multi Scale Problems and Asymptotic Analysis, GAKUTO Internat. Ser. Math. Sci. Appl, vol.24, pp.153-165, 2005.

). D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order Reprint of the 1998 edition, Classics in Mathematics, 2001.

S. M. Kozlov, Reducibility of quasiperiodic differential operators and averaging. (Russian) Trudy Moskov, Mat. Obshch, pp.46-99, 1983.

O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Ural-'ceva, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs, vol.23, 1967.

). I. Pankratova and A. Piatnitski, On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder, Discrete and Continuous Dynamical Systems - Series B, vol.11, issue.4, 2009.
DOI : 10.3934/dcdsb.2009.11.935

). A. Piatnitski, AVERAGING A SINGULARLY PERTURBED EQUATION WITH RAPIDLY OSCILLATING COEFFICIENTS IN A LAYER, Mathematics of the USSR-Sbornik, vol.49, issue.1, pp.19-40, 1984.
DOI : 10.1070/SM1984v049n01ABEH002694

). V. Zhikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of differential operators and integral functionals 33 PAPER F PAPER F Homogenization of spectral problem for periodic elliptic operators with sign-changing density function S, p.3, 1994.

). G. Allaire and A. Piatnitski, UNIFORM SPECTRAL ASYMPTOTICS FOR SINGULARLY PERTURBED LOCALLY PERIODIC OPERATORS, Communications in Partial Differential Equations, vol.90, issue.4, pp.3-4, 2002.
DOI : 10.1081/PDE-120002871

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.629

). G. Allaire, Y. Capdeboscq, A. Piatnitski, V. Siess, and M. Vanninathan, Homogenization of Periodic Systems with Large Potentials, Archive for Rational Mechanics and Analysis, vol.90, issue.2, pp.179-220, 2004.
DOI : 10.1007/s00205-004-0332-7

M. S. Birman and M. Z. Solomyak, Spectral Theory of Self-Adjoint Operators in Hilbert Space, 1987.
DOI : 10.1007/978-94-009-4586-9

G. Cardone, A. Esposito, and S. A. Nazarov, Korn's inequality for periodic solids and convergence rate of homogenization (submitted)

). D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition, Classics in Mathematics, 2001.

). S. Kesavan, Homogenization of Elliptic Eigenvalue Problems: Part 1, Appl. Math. Optim, issue.05336175, pp.153-167, 1979.

). S. Kesavan, Homogenization of Elliptic Eigenvalue Problems: Part 2, Appl. Math. Optim, issue.05336175, pp.197-216, 1979.

S. A. Nazarov, Asymptotic analysis of thin plates and rods, p.2002

S. A. Nazarov, Asymptotics of negative eigenvalues of a Dirichlet problem with sign-changing density function Trudy seminara I.G.Petrovskogo, p.28, 2009.

S. A. Nazarov and A. L. Piatnitski, Homogenization of the spectral Dirichlet problem for a system of differential equations with rapidly oscillating coefficients and changing sign sensity. (English), Journal of Mathematical Sciences, vol.169, issue.2, p.212248, 2010.

). O. Oleinik, G. A. Yosifian, and A. S. Shamaev, Mathematical problems in elasticity and homogenization, Studies in Mathematics and its Applications, 1992.

M. I. Visik and L. A. Lyusternik, Regular degeneration and boundary layer for linear differential equations with small parameter, Nauk (N.S.), vol.12, issue.577, pp.3-122, 1957.

). V. Zhikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of differential operators and integral functionals, 1994.

). T. Ya, I. S. Azizov, and . Iokhvidov, Linear operators in spaces with an indefinite metric, 1989.

I. C. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, vol.18, 1969.

). S. Kesavan, Homogenization of Elliptic Eigenvalue Problems: Part 1, Appl. Math. Optim, issue.05336175, pp.153-167, 1979.

). S. Kesavan, Homogenization of Elliptic Eigenvalue Problems: Part 2, Appl. Math. Optim, issue.05336175, pp.197-216, 1979.

V. P. Mihailov and S. G. Mihlin, Partial differential equations Mathematical physics, an advanced course English transl. North-Holland Ser. in Appl, Nauka, Moscow) Math. Mech, issue.10 11, 1968.

S. A. Nazarov and A. L. Piatnitski, Homogenization of a spectral Dirichlet problem for a system of differential equation with highly-oscillating coefficients in the case of the sign-changing density, R&D Report, issue.2, 2009.

S. A. Nazarov, I. L. Pankratova, A. L. Piatnitski, and R. Report, Homogenization of spectral problem for periodic elliptic operators with sign-changing weight function, 2008.

). O. Oleinik, G. A. Yosifian, and A. S. Shamaev, Mathematical problems in elasticity and homogenization, Studies in Mathematics and its Applications, 1992.

). I. Pankratova and A. Piatnitski, On the behaviour at infinity of solutions to stationary convectiondiffusion equation in a cylinder, DCDS-B, vol.11, issue.4, 2009.

L. S. Pontrjagin, Hermitian operators in spaces with indefinite metric, Russian) Bull. Acad. Sci. URSS. Ser. Math. [Izvestia Akad. Nauk SSSR] 8, pp.243-280, 1944.

). S. Pyatkov and . Operator, Nonclassical problems. Inverse and Ill-posed Problems Series, VSP, 2002.

M. I. Visik and L. A. Lyusternik, Regular degeneration and boundary layer for linear differential equations with small parameter, Nauk (N.S.), vol.12, issue.577, pp.3-122, 1957.

). V. Zhikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of differential operators and integral functionals, 1994.

). V. Zhikov, On an extension of the method of two-scale convergence and its applications, Sbornik: Mathematics, vol.191, issue.7, pp.973-1014, 2000.
DOI : 10.1070/SM2000v191n07ABEH000491