Removable singularities of solutions to a class of quasilinear non- uniformly elliptic equations
type: Item
instance of: scholarly article
title: Removable singularities of solutions to a class of quasilinear non- uniformly elliptic equations
zbMATH Open document ID: 0655.35020
DOI: 10.1016/0022-0396(88)90024-1
author: Chi-Ping Lau
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: Let \(\Omega\) be a bounded domain of \({\mathbb{R}}^ n,\) \(n\geq 2\), and K be a compact subset of \(\Omega\). Suppose \(u\in C^ 2(\Omega/k)\) satisfies the quasilinear equations: \[ (1)\quad div A(x,Du)=B(x,u). \] Here \(A=(A_ 1,...,A_ n)\) is a given vector-valued function of \((x,p)\in \Omega \times {\mathbb{R}}^ n\) and B is a given scalar function. Under some conditions on A, B and K, the author proves that u can be defined on K so that the resulting function is a C 2 solution of (1) in all of \(\Omega\). In which the singular set K can indeed be allowed to approach the boundary and some interesting examples are given.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J67
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 4069409
zbMATH Keywords: quasilinear
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90024-1
OpenAlex ID: W2093954391
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description: scientific article; zbMATH DE number 4069409