Principle of additivity in averaging of degenerate nonlinear Dirichlet problems - Larin, D. V.; Skrypnik, I. V. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
We study the problem of averaging of Dirichlet problems for degenerate nonlinear elliptic equations of the second order in domains with fine-grained boundary under the condition that the weight function belongs to a certain Muckenhoupt class. We prove a pointwise estimate for solutions of the model degenerate nonlinear problem. The averaged boundary-value problem is constructed under new structural conditions for a perforated domain. In particular, we do not assume that the diameters of cavities are small as compared with the distances between them.