Asymptotic behaviour of nonlinear Dirichlet problems in perforated domains
type: Item
instance of: scholarly article
title: Asymptotic behaviour of nonlinear Dirichlet problems in perforated domains
zbMATH Open document ID: 0991.35034
DOI: 10.1007/BF01759365
author: G. Dal Maso
author: Igor V. Skrypnik
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2002-09-01T00:00:00Z
review text: The authors consider the sequence of boundary value problems: \[ \begin{cases} \sum^N_{j=1} {\partial\over \partial x_j}\left( a_j\left( x,u_s(x), {\partial u_s(x) \over\partial x}\right) \right)= a_0\left( x,u_s(x), {\partial u_s(x) \over\partial x}\right) \text{ in }\Omega\\ u_s(x)= f(x)\text{ in } \partial \Omega_s,\end{cases} \] where \(s=1,2,\dots\) and \(\Omega_s\) is an arbitrary sequence of open subsets of bounded set \(\Omega\subset \mathbb{R}^N\). The goal of this paper is to study the asymptotic behaviour of \(u_s(x)\) as \(s\to\infty\) under very weak assumptions on the sets \(\Omega_s\), that is under very mild assumptions on the capacity of the holes.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1463337
zbMATH Keywords: weak solution
zbMATH Keywords: capacity of the holes
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01759365
OpenAlex ID: W1966095551
description: scientific article; zbMATH DE number 1463337