Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains
Annales de l'I.H.P. Analyse non linéaire, Volume 21 (2004) no. 4, pp. 445-486.
@article{AIHPC_2004__21_4_445_0,
     author = {Dal Maso, Gianni and Murat, Fran\c{c}ois},
     title = {Asymptotic behaviour and correctors for linear {Dirichlet} problems with simultaneously varying operators and domains},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {445--486},
     publisher = {Elsevier},
     volume = {21},
     number = {4},
     year = {2004},
     doi = {10.1016/j.anihpc.2003.05.001},
     zbl = {1110.35008},
     mrnumber = {2069633},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2003.05.001/}
}
TY  - JOUR
AU  - Dal Maso, Gianni
AU  - Murat, François
TI  - Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2004
DA  - 2004///
SP  - 445
EP  - 486
VL  - 21
IS  - 4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2003.05.001/
UR  - https://zbmath.org/?q=an%3A1110.35008
UR  - https://www.ams.org/mathscinet-getitem?mr=2069633
UR  - https://doi.org/10.1016/j.anihpc.2003.05.001
DO  - 10.1016/j.anihpc.2003.05.001
LA  - en
ID  - AIHPC_2004__21_4_445_0
ER  - 
%0 Journal Article
%A Dal Maso, Gianni
%A Murat, François
%T Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains
%J Annales de l'I.H.P. Analyse non linéaire
%D 2004
%P 445-486
%V 21
%N 4
%I Elsevier
%U https://doi.org/10.1016/j.anihpc.2003.05.001
%R 10.1016/j.anihpc.2003.05.001
%G en
%F AIHPC_2004__21_4_445_0
Dal Maso, Gianni; Murat, François. Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains. Annales de l'I.H.P. Analyse non linéaire, Volume 21 (2004) no. 4, pp. 445-486. doi : 10.1016/j.anihpc.2003.05.001. http://www.numdam.org/articles/10.1016/j.anihpc.2003.05.001/

[1] Ansini N, Braides A, Separation of scales and almost-periodic effects in the asymptotic behaviour of perforated periodic media, Acta Appl. Math. 65 (2001) 59-81. | MR | Zbl

[2] Bensoussan A, Boccardo L, Dall'Aglio A, Murat F, H-convergence for quasilinear elliptic equations under natural hypotheses on the correctors, in: Proceedings of the Second Workshop on Composite Media and Homogenization Theory (Trieste, 1993), World Scientific, Singapore, 1995, pp. 93-112.

[3] Bensoussan A, Lions J.-L, Papanicolaou G, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978. | MR | Zbl

[4] Boccardo L, Murat F, Nouveaux résultats de convergence dans des problèmes unilatéraux, in: Nonlinear Partial Differential Equations and Their Applications, Collège de France Seminar, vol. II, Res. Notes Math., vol. 60, Pitman, London, 1982, pp. 64-85. | MR | Zbl

[5] Buttazzo G, Dal Maso G, Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions, Appl. Math. Optim. 23 (1991) 17-49. | MR | Zbl

[6] Calvo Jurado C, Casado Diaz J, The limit of Dirichlet systems for variable monotone operators in general perforated domains, J. Math. Pures Appl. 81 (2002) 471-493. | MR | Zbl

[7] Cioranescu D, Murat F, Un terme étrange venu d'ailleurs, I, in: Nonlinear Partial Differential Equations and Their Applications, Collège de France Seminar, vol. II, Res. Notes Math., vol. 60, Pitman, London, 1982, pp. 98-138. | MR | Zbl

[8] Dall'Aglio A, Murat F, A corrector result for H-converging parabolic problems with time-dependent coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997) 423-464. | Numdam | MR | Zbl

[9] Dal Maso G, On the integral representation of certain local functionals, Ricerche Mat. 32 (1983) 85-113. | MR | Zbl

[10] Dal Maso G, Γ-convergence and μ-capacities, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987) 423-464. | Numdam | Zbl

[11] Dal Maso G, Garroni A, New results on the asymptotic behaviour of Dirichlet problems in perforated domains, Math. Models Methods Appl. Sci. 4 (1994) 373-407. | MR | Zbl

[12] Dal Maso G, Malusa A, Approximation of relaxed Dirichlet problems by boundary value problems in perforated domains, Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 99-114. | MR | Zbl

[13] Dal Maso G, Mosco U, Wiener criteria and energy decay for relaxed Dirichlet problems, Arch. Rational Mech. Anal. 95 (1986) 345-387. | MR | Zbl

[14] Dal Maso G, Mosco U, Wiener's criterion and Γ-convergence, Appl. Math. Optim. 15 (1987) 15-63. | Zbl

[15] Dal Maso G, Murat F, Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (1997) 239-290. | Numdam | MR | Zbl

[16] Evans L.C, Gariepy R.F, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992. | MR | Zbl

[17] Heinonen J, Kilpeläinen T, Martio O, Nonlinear Potential Theory of Degenerate Elliptic Equations, Clarendon Press, Oxford, 1993. | MR | Zbl

[18] Kovalevsky A, An effect of double homogenization for Dirichlet problems in variable domains of general structure, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 1151-1156. | MR | Zbl

[19] Maz'Ya V.G, Sobolev Spaces, Springer-Verlag, Berlin, 1985. | MR | Zbl

[20] Meyers N.G, An Lp-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 17 (1963) 189-206. | Numdam | MR | Zbl

[21] Murat F, L'injection du cône positif de H−1 dans W−1,q est compacte pour tout q<2, J. Math. Pures Appl. 60 (1981) 309-322. | Zbl

[22] F. Murat, H-convergence, Séminaire d'Analyse Fonctionnelle et Numérique, Université d'Alger, 1977-1978, multicopied, 34 pp..

[23] Sanchez-Palencia E, Non Homogeneous Media and Vibration Theory, Lecture Notes in Phys., vol. 127, Springer-Verlag, Berlin, 1980. | MR | Zbl

[24] Spagnolo S, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 22 (1968) 577-597. | Numdam | MR | Zbl

[25] Stampacchia G, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble) 15 (1965) 189-258. | Numdam | MR | Zbl

[26] Homogénéisation et compacité par compensation, Cours Peccot, Collège de France, March 1977, partially written in [22].

[27] Ziemer W.P, Weakly Differentiable Functions, Springer-Verlag, Berlin, 1989. | MR | Zbl

Cited by Sources: