Homogenization of general quasi-linear Dirichlet problems with quadratic growth in perforated domains
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.
scientific article; zbMATH DE number 1057128
scientific article