Nonlinear elliptic equations in \(\mathbb{R}^ N\) without growth restrictions on the data
type: Item
instance of: scholarly article
title: Nonlinear elliptic equations in \(\mathbb{R}^ N\) without growth restrictions on the data
zbMATH Open document ID: 0810.35021
author: Juan Luis Vázquez
author: Lucio Boccardo
author: T. Gallouët
published in: Journal of Differential Equations
publication date: 1995-04-10T00:00:00Z
review text: The authors examine equations of the form (*) \(-\text{div } A(x,Du)+ g(x,u) =f\), where the principal part of the operator, \(-\text{div } A(x,Du)\) acts like the \(p\)-Laplacian. Provided \(ug(x,u)\) goes to infinity fast enough as \(| u|\to\infty\), they show that equation (*) has a distributional solution in \(\mathbb{R}^ N\) for any locally integrable function \(f\). In addition, the gradient of this solution, which is only assumed to be locally in \(L^{p-1}\), is locally in \(L^ q\) for some \(q>p-1\); the exponent \(q\) is given explicitly in terms of \(p\), \(N\), and the growth of \(g\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 439984
zbMATH Keywords: estimates of the gradient
zbMATH Keywords: \(p\)-Laplacian
reviewed by: Gary M. Lieberman
MaRDI profile type: Publication
full work available at URL: jdeq.1993.1092
OpenAlex ID: W1974720859
DOI: 10.1006/JDEQ.1993.1092
description: scientific article; zbMATH DE number 439984