Strong stability results for solutions of elliptic equations with power-like lower order terms and measure data
type: Item
instance of: scholarly article
title: Strong stability results for solutions of elliptic equations with power-like lower order terms and measure data
zbMATH Open document ID: 1012.35030
author: Luigi Orsina
author: Alain Prignet
published in: Journal of Functional Analysis
publication date: 2002-09-08T00:00:00Z
review text: This paper deals with extending a well-known result by H. Brezis to the nonlinear case, namely: Let \(u_n\) be the sequence of solutions of \[ \begin{cases} -\text{div} \bigl(a(x,u_n, \nabla u_n) \bigr)+ |u_n|^{q-1} \cdot u_n=f_n \quad &\text{in }\Omega\\ u_n=0 \quad &\text{on }\partial \Omega, \end{cases} \tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\), and \(f_n\) is a sequence of functions which is strongly convergent to a function \(f\) in \(L^1_{\text{loc}}(\Omega \setminus K)\), with \(K\) compact in \(\Omega\) of zero \(r\)-capacity; no assumptions are made on \(f_n\) on the set \(K\). Under some suitable additional assumptions on the data of (1), the authors show that \(u_n\) converges to \(u\), which verifies the same problem with datum \(f\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 1797581
zbMATH Keywords: strong stability
zbMATH Keywords: elliptic equation with power-line lower order term
zbMATH Keywords: measure data
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W2053294706
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DOI: 10.1006/JFAN.2001.3846
description: scientific article; zbMATH DE number 1797581