Larin D. Homogenization of degenerate nonlinear problems in perforated domains

The questions of homogenization of a family Dirich let problems for degenerate nonlinear elliptic second order equations in domains with a finely granulated boundary and in perforated domains with densely pac king "grains" provided that the weight function be longs to a certain Muckenhoupt class are investigated. The asymptotic behavior of a sequences of solutions of problems under consideration is studied. Sufficient conditions of convergence of solutions are obtained. Boundary value problems for the limit functions are constructed. The results are based on a various pointwise estimates of a solution of a special model degenerate nonlinear Dirichlet problem.