Non-uniformly elliptic equations with natural growth in the gradient
type: Item
instance of: scholarly article
title: Non-uniformly elliptic equations with natural growth in the gradient
zbMATH Open document ID: 1040.35010
DOI: 10.1023/A:1021884903872
author: Cristina Trombetti
published in: Potential Analysis
publication date: 2003-04-27T00:00:00Z
review text: Existence of bounded solutions for a class of nonlinear elliptic problems of type \[ -\text{div\,} (a(x,u,Du))=H(x,u,Du) +f,\qquad u\in W^{1,p}_0(\Omega)\cap L^\infty(\Omega), \] where \(\langle a(x,\eta,\xi),\xi\rangle\geq b(| \eta| )| \xi| ^p,\) \(b\) is a continuous monotone decreasing function and \(| H(x,\eta,\xi)| \leq k(\eta)| \xi| ^p,\) \(k\) is a continuous monotone increasing function, is proved.
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 1901245
zbMATH Keywords: existence
zbMATH Keywords: nonlinear elliptic equations
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: a:1021884903872
OpenAlex ID: W1549042289
description: scientific article; zbMATH DE number 1901245