Interface problems for quasilinear elliptic equations
type: Item
instance of: scholarly article
title: Interface problems for quasilinear elliptic equations
zbMATH Open document ID: 0940.35081
published in: Journal of Differential Equations
publication date: 2000-06-20T00:00:00Z
review text: Let \(\Omega\subset{\mathbb R}^2\) be a polygonal domain whose closure is the union of the closures of finitely many polygonal subdomains \(\Omega^{(k)}\). The author studies the uniformly elliptic Dirichlet problem \[ -D_i[A^{ij}(x,u)D_j]=-D_iF^I\quad \text{on }\Omega, \qquad u|\partial\Omega=0 \] assuming that \(A^{ij}|[\text{cl}(\Omega^{(k)})\times{\mathbb R}]\in C^1(\text{cl}(\Omega^{(k)})\times{\mathbb R})\) and \(F^i\in H^1(\Omega)\cap C^{0,\sigma}(\Omega)\). Roughly speaking, he establishes \(H^2\cap C^{1,\sigma}\)-interior regularity in \(\Omega^{(k)}\) for bounded weak solutions and obtains then a representation of a solution near a singular point in terms of particular solutions.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J99
Mathematics Subject Classification ID: 35C99
zbMATH DE Number: 1346394
zbMATH Keywords: polygonal domain
zbMATH Keywords: uniformly elliptic Dirichlet problem
zbMATH Keywords: interior regularity
zbMATH Keywords: singular point
zbMATH Keywords: particular solutions
author: Jinbiao Wu
reviewed by: Georg Hetzer
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3622
OpenAlex ID: W2001303543
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DOI: 10.1006/JDEQ.1998.3622
description: scientific article; zbMATH DE number 1346394