References
- Calvo-Jurado , C. , Casado-Díaz , J. and Laynez , M. L. Homogenization of nonlinear elliptic problems with varying boundary conditions on varying domains . Submitted for publication
- Calvo-Jurado , C. and Casado-Díaz , J. 2002 . The limit of Dirichlet systems for variable monotone operators in general perforated domains . Journal de Mathématiques Pures et Appliquées , 81 : 471 – 493 .
- Casado-Díaz , C. 1997 . Homogenization of general quasi-linear Dirichlet problems with quadratic growth in perforated domains . Journal de Mathématiques Pures et Appliquées , 76 : 431 – 476 .
- Casado-Díaz , J. 1997 . Homogenization of Dirichlet problems for monotone operators in varying domains . Proceedings of the Royal Society, Edinburgh A , 127 : 457 – 478 .
- Casado-Diaz , J. and Garroni , A. 2000 . Asymptotic behaviour of nonlinear elliptic systems on varying domains . SIAM Journal of Mathematical Analysis , 31 ( 3 ) : 581 – 624 .
- Cioranescu , D. and Murat , F. 1982 . “ Un terme étrange venu d'ailleurs ” . In Nonlinear Partial Differential Equations and their Applications , Edited by: Brézis , H. and Lions , J. L. 98 – 138 . 154 – 78 . London : Pitman . Collège de France seminar, Vols II and III. Research Notes in Mathematics 60 and 70
- Dal Maso , G. and Defranceschi , A. 1988 . Limits of nonlinear Dirichlet problems in varying domains . Manuscripta Mathematica , 61 : 251 – 278 .
- Dal Maso , G. and Garroni , A. 1994 . New results on the asymptotic behaviour of Dirichlet problems in perforated domains . Mathematical Models & Methods in Applied Sciences , 3 : 373 – 407 .
- Dal Maso , G. , Garroni , A. and Skrypnik , I. V. 1997 . A capacity method for the asymptotic analysis of Dirichlet problems for monotone operators . Journal of Mathematical Analysis and Applications , 71 : 263 – 313 .
- Dal Maso , G. and Mosco , U. 1987 . Wiener-criterion and Γ-convergence . Applied Mathematics and Optimization , 15 : 15 – 63 .
- Dal Maso , G. and Murat , F. 1997 . Asymptotic behaviour and correctors for the Dirichlet problems in perforated domains with homogeneous monotone operators . Annali della Scuola Normale Superiore di Pisa , 7 ( 4 ) : 765 – 803 .
- Dal Maso , G. and Murat , F. 2004 . Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains . Annales de l'Institut Henri Poincaré. Analyse Non Linéaire , 21 ( 4 ) : 445 – 486 .
- Skrypnik , I. V. 1993 . Asymptotic behaviour of solutions of nonlinear elliptic problems in perforated domains . Matematicheskiui Sbornik , 184 ( 10 ) : 67 – 90 .
- Skrypnik , I. V. 1995 . Averaging of quasilinear parabolic problems in domains with fine-grained boundary . Differential Equations , 31 ( 2 ) : 327 – 339 .
- Calvo-Jurado , C. and Casado-Díaz , J. Homogenization of Dirichlet parabolic systems with variable monotone operators in general perforated domains . Proceedings of the Royal Society . Edinburgh. Vol. 133A , pp. 1231 – 1248 .
- Lurie , K. A. 1993 . Applied Optimal Control Theory of Distributed Systems , New York : Plenum Press .
- Murat , F. 1972 . Théorèmes de non-existence pour des problèmes de contrôle dans le coefficients . Comptes Rendus Mathématique. Académie des Sciences, Paris A , 274 : 395 – 398 .
- Buttazzo , G. and Dal Maso , G. 1991 . Shape optimization for Dirichlet problems, Relaxed SIS and optimal conditions . Applied Mathematics and Optimization , 23 : 17 – 49 .
- Buttazzo , G. , Dal Maso , G. , Garroni , A. and Malusa , A. 1997 . On the relaxed formulation of some shape optimization problems . Advances in Mathematical Sciences and Applications 7 , 1 : 1 – 24 .
- Allaire , G. 2002 . Shape Optimization by the Homogenization Method. Applied Mathematical Sciences , Vol. 146 , New York : Springer Verlag .
- Evans , L. C. and Gariepy , R. F. 1992 . Measure Theory and Fine Properties of Functions , Boca Raton : CRC Press .
- Ziemer , W. P. 1989 . Weakly Differentiable Functions , Berlin : Springer Verlag .