A degenerate quasi-linear Dirichlet problem for domains with a fine-grained boundary. The case of surface distribution of ``grains''
type: Item
instance of: scholarly article
zbMATH Open document ID: 0973.35030
author: Dmitry V. Larin
publication date: 2001-09-23T00:00:00Z
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 1641407
zbMATH Keywords: nonlinear elliptic equation
zbMATH Keywords: Muckenhoupt class
zbMATH Keywords: perforated domain
zbMATH Keywords: degeneration
zbMATH Keywords: asymptotic behaviour
MaRDI profile type: Publication
title: A degenerate quasi-linear Dirichlet problem for domains with a fine-grained boundary. The case of surface distribution of ``grains''
published in: Trudy Instituta Prikladnoĭ Matematiki i Mekhaniki
review text: 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.
reviewed by: A. G. Shchelkov
description: scientific article; zbMATH DE number 1641407