Abstract
We describe the asymptotic behaviour of the solution of a quasi-linear elliptic problem posed in a domain of , and with homogeneous Dirichlet boundary conditions imposed on small zones of size less than ε distributed on the boundary of this domain when the parameter ε goes to 0. We use epi-convergence arguments in order to establish the limit behaviour
References
- H. Attouch: Variational Convergence for Functions and Operators, Pitman, London, 1984.Google Scholar
- H. Attouch, C. Picard: Problèmes variationnels et théorie du potentiel non linéaire, Ann. Fac. Sci. Toulouse. 1 (1979) 89-136.https://doi.org/10.5802/afst.532Google Scholar
- H. Attouch, C. Picard: Comportement limite de problèmes de transmission unilatéraux à travers des grilles de forme quelconque, Rend. Sem. Mat. Univ. Politec. Torino 45(1) (1987) 71-85.Google Scholar
- H. Attouch, C. Picard: Variational inequalities with varying obstacles, J. Func. Analysis 50 (1983) 329-386.https://doi.org/10.1016/0022-1236(83)90009-5Google Scholar
- D. Cioranescu, F. Murat: Un terme étrange venu d'ailleurs, Collège de France Seminar Nonlinear PDE, Research Notes in Maths. 60, Pitman, London (1982) 98-138.Google Scholar
- G. Dal Maso: On the integral representation of certain local functionals, Ricerche Mat. 32 (1983) 85-113.Google Scholar
- E. De Giorgi: Convergence problems for functionals and operators, In: Proc. of the Inter. Meeting on Recent Methods in Nonlinear Analysis, Rome, 1978, De Giorgi et al. (eds.), Pitagora Editrice, Bologna, (1979) 131-188.Google Scholar
- E. De Giorgi, T. Franzoni: Su un tipo di convergenza variazionale, Rend. Accad. Naz. Lincei. 58 (1975) 842-850.Google Scholar
- M. El Jarroudi: Homogénéisation par Épi-convergence de Quelques Problèmes de la Mécanique des Milieux Continus, Thèse de Doctorat, Université de Haute-Alsace, 1994.Google Scholar
- J. Frehse: Capacity methods in the theory of partial differential equations, Jahresber. der Deutschen Math. Verein. 84 (1982) 1-44.Google Scholar
- N. Labani: Thèse de 3ème cycle, Université Paris Sud Orsay, 1987.Google Scholar
- M. Lobo, M. E. Perez: Boundary homogenization of certain elliptic problems for cylindrical bodies, Bull. Sci. Math. 116 (1992) 399-426.Google Scholar
- J. Necas: Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris, 1967.Google Scholar
Suggested citation
Published by Heldermann Verlag, 1999. Rights now held by Banach Press LLC.
