Boundedness and regularity of solutions of degenerate elliptic partial differential equations
type: Item
instance of: scholarly article
title: Boundedness and regularity of solutions of degenerate elliptic partial differential equations
zbMATH Open document ID: 1377.35047
author: Seng-Kee Chua
published in: Journal of Differential Equations
publication date: 2017-08-03T00:00:00Z
review text: The paper under review deals with suitably defined weak solutions to the equation \[ \sum_{i,j}\frac{\partial}{\partial x_i}\left(B_{ij}(x,u,\nabla u)\frac{\partial}{\partial x_j}u\right)+g(x,u,\nabla u)=0, \] where \(x\) belongs to an open set \(\Omega\) in an \(n\)-dimensional metric space \(X\) and the \(n\times n\) matrix-valued function \(B=\{B_{ij}\}\) is nonnegatively definite. By applying the Moser iterations, the author proves local boundedness of the solutions when a weighted Sobolev embedding holds on \(X\). Moreover, a Harnack type inequality for the nonnegative solutions is obtained assuming a weighted version of the Poincaré for their logarithm.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 6756298
zbMATH Keywords: local boundedness
zbMATH Keywords: Hölder continuity
zbMATH Keywords: Harnack inequality
zbMATH Keywords: Moser iterations
zbMATH Keywords: weighted Sobolev embedding
MaRDI profile type: Publication
full work available at URL: j.jde.2017.05.001
OpenAlex ID: W2618144884
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DOI: 10.1016/J.JDE.2017.05.001
description: scientific article; zbMATH DE number 6756298