Homogenization of general quasi-linear Dirichlet problems with quadratic growth in perforated domains
type: Item
instance of: scholarly article
title: Homogenization of general quasi-linear Dirichlet problems with quadratic growth in perforated domains
zbMATH Open document ID: 0880.35015
DOI: 10.1016/S0021-7824(97)89958-8
author: Juan Casado-Díaz
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1998-01-28T00:00:00Z
review text: We study the homogenization in a sequence of perforated domains of the Dirichlet problem corresponding to the perturbation of the Poisson equation by a nonlinear term which has a growth at most quadratic in the gradient. As in the linear case, we prove that a new term appears in the limit problem which does not depend on the gradient but now it becomes nonlinear. This means that the nonlinear perturbation changes the structure of the limit problem for the Poisson equation and that the behaviour of the corresponding solutions for both, the linear and nonlinear problem are different. However, the proof of our result is based on a comparison between the solutions to the nonlinear problem and the corrector to the Poisson problem. A corrector result is also obtained.
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1057128
zbMATH Keywords: Poisson equation
zbMATH Keywords: nonlinear perturbation
MaRDI profile type: Publication
cites work: Q5186236
cites work: Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions
cites work: Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations
cites work: Q3715516
cites work: Q3837267
cites work: Homogenization of a quasi-linear problem with quadratic growth in perforated domains: An example
cites work: Homogenisation of Dirichlet problems for monotone operators in varying domains
cites work: Asymptotic Behavior of Nonlinear Elliptic Systems on Varying Domains
cites work: Q3961204
cites work: NEW RESULTS ON THE ASYMPTOTIC BEHAVIOR OF DIRICHLET PROBLEMS IN PERFORATED DOMAINSDIRICHLET PROBLEMS IN PERFORATED DOMAINS
cites work: Q4369312
cites work: Q4371385
cites work: Les potentiels d'energie finie
cites work: Q3029673
cites work: Q5648620
cites work: Q4009488
cites work: Quasi-Linear Relaxed Dirichlet Problems
cites work: Q4205790
cites work: Q3977474
cites work: SOME PROPERTIES OF THE SPECTRUM OF NONLINEAR EQUATIONS OF STURM-LIOUVILLE TYPE
cites work: The homogenization of nonlinear Dirichlet problems in perforated domains of general structure
cites work: Change of variables for absolutely continuous functions
description: scientific article; zbMATH DE number 1057128