Homogenization of a quasi-linear problem with quadratic growth in perforated domains: An example
This paper is related to the homogenization of a Dirichlet problem. A perturbation of the Laplace operator is considered for a series of domains which varies arbitrarily. As consequence, a new nonlinear term appears in the homogenized problem. A comparison is made with the well known result of \textit{D. Cioranescu} and \textit{F. Murat} [Res. Notes. Math. 60, 98-138 (1982; Zbl 0496.35030)]. To obtain the result, a changement of the unknown function is made and the solution of the linear problem is used to pass to the limit. A Borel measure is also defined by using the limit of the solution of a particular Dirichlet problem. In the last part a corrector result is given and a comparison is made with the case of oscillating coefficients.
scientific article; zbMATH DE number 1080028
scientific article