Some regularity results for nonlinear degenerate elliptic equations
type: Item
instance of: scholarly article
title: Some regularity results for nonlinear degenerate elliptic equations
zbMATH Open document ID: 0826.35039
author: G. Rita Cirmi
published in: Differential and Integral Equations
publication date: 1995-11-23T00:00:00Z
review text: The author studies regularity of solutions of the homogeneous Dirichlet problem for nonlinear partial differential operators of the form \(Au = - \text{div} (a (x,u, Du))\). A is not uniformly elliptic, but satisfies the condition \(a(x,s,\xi) \xi \geq \nu (x) |\xi |^p\), where \(\nu\) is a nonnegative function in \(L^1 (\Omega)\), \(p > 1\). The main results of the paper state that any solution of the equation \(Au = f\) lies in \(L^{\widehat p} (\Omega)\), where \(\widehat p\) depends on \(p,f\), and the dimension \(n\).
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 716209
zbMATH Keywords: nonlinear degenerate elliptic equations
zbMATH Keywords: \(L^ p\)-regularity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 716209