A priori estimates for solutions to nonlinear elliptic equations
type: Item
instance of: scholarly article
title: A priori estimates for solutions to nonlinear elliptic equations
zbMATH Open document ID: 0807.35040
DOI: 10.1007/BF00378165
author: Wenxiong Chen
author: Congming Li
published in: Archive for Rational Mechanics and Analysis
publication date: 1993-09-07T00:00:00Z
review text: The paper treats the Dirichlet problem for a two-dimensional semilinear elliptic partial differential equation involving the Laplacian. The domain is assumed to be bounded and smooth. In the case of a nonlinear term with exponential growth the authors establish interior and boundary \(L^ \infty\)-a priori estimates. The interior estimates are obtained by following a ``blow-up'' idea of Brezis and Merle whereas the boundary estimates are proved by using the method of moving planes. The results give a partial answer to a problem posed by Brezis and Merle.
reviewed by: J.Madjarova
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 410079
zbMATH Keywords: \(L^ \infty\)-a priori estimates
zbMATH Keywords: two-dimensional semilinear elliptic partial differential equation
zbMATH Keywords: method of moving planes
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00378165
OpenAlex ID: W2001046876
description: scientific article; zbMATH DE number 410079