Homogenization of non-linear Dirichlet problems in perforated domains of general type
Igor Vladimirovich Skrypnik · Sbornik Mathematics · 1996
A sequence of boundary-value problems for a second-order non-linear elliptic equation in domains and is considered. No geometric assumptions on the are made. The existence of a sequence approaching zero as is assumed such that for and for an arbitrary point . Here is the -cube with centre at and is the -capacity. The conditions imposed on the coefficients of the equation ensure that the energy space is . The strong convergence of the solutions of the problems under consideration is proved in for ; a corrector in and a homogenized boundary-value problem are constructed. These results are based on an asymptotic expansion for the sequence and on a new pointwise estimate of the solution of a certain model non-linear problem.