Degenerate nonlinear higher-order elliptic problems in domains with fine-grained boundary

We study the convergence of the solutions of the Dirichlet problem associated to a degenerate nonlinear higher-order elliptic equations in divergence form in variables domains, to a limit solution of the same type problem in a fixed domain, following the methods of the asymptotic expansion developed by Skrypnik [Methods for Analysis of Nonlinear Elliptic Boundary Value Problems, AMS, Providence, RI, 1994] modified to weighted higher-order case.