\(L^r\) estimates for degenerate elliptic problems
type: Item
instance of: scholarly article
title: \(L^r\) estimates for degenerate elliptic problems
zbMATH Open document ID: 1014.35035
DOI: 10.1023/A:1014895230754
author: N. Grenon
published in: Potential Analysis
publication date: 2002-08-21T00:00:00Z
review text: This paper deals with \(L^r\) estimates for degenerate elliptic problems, that is \[ -\text{div} \bigl(a(x,u,Du) \bigr)=f,\tag{1} \] with \(f\) in \(L^q\) for \(q\in [1,\infty)\), where the operator \(a(x,u,Du)\) satisfies \[ \alpha \bigl(|s|\bigr)|\xi|^p \leq\bigl(a (x,s,\xi), \xi\bigr) \quad \text{with }p>1. \tag{2} \] The author proves \(L^r\) estimates for the Dirichlet problem of (1) without symmetrization, which are sharp in some sense.
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 1785620
zbMATH Keywords: degenerate elliptic problems
zbMATH Keywords: symmetrization
zbMATH Keywords: \(L^r\) estimates
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1785620