A degenerate quasi-linear Dirichlet problem for domains with a fine-grained boundary. The case of surface distribution of ``grains''
The paper is devoted to the questions of homogenization of a family of Dirichlet problems for degenerate nonlinear second-order equations in domains with a finely granulated boundary in a case of concentration of such boundary near some smooth surface provided that the weight function belongs to certain Muckenhoupt class. The asymptotic behaviour of a sequence of solutions of problems under consideration is studied and sufficient conditions of convergence are obtained. A corrector for approximation of such sequence of solutions and a boundary-value problem for the limit function are constructed. NEWLINENEWLINENEWLINEThe results are based on a pointwise estimate of solution of a model degenerate nonlinear Dirichlet problem.
scientific article; zbMATH DE number 1641407