Existence of solutions for degenerate elliptic problems in weighted Sobolev space
type: Item
instance of: scholarly article
title: Existence of solutions for degenerate elliptic problems in weighted Sobolev space
zbMATH Open document ID: 1332.35124
DOI: 10.1155/2015/265127
author: Lili Dai
author: Zhongqing Li
author: Wenjie Gao
published in: Journal of Function Spaces
publication date: 2016-01-12T00:00:00Z
review text: Summary: This paper is devoted to the study of the existence of solutions to a general elliptic problem \(Au+g(x,u,\nabla u)=f-\mathrm{div} F\), with \(f\in L^1(\Omega)\) and \(F\in\prod_{i=1}^NL^{p'}(\Omega,\omega_i^\ast)\), where \(A\) is a Leray-Lions operator from a weighted Sobolev space into its dual and \(g(x,s,\xi)\) is a nonlinear term satisfying \(g(x,s,\xi)\mathrm{sgn}(s)\geq\rho\sum_{i=1}^N\omega_i|\xi_i|p\), \(|s|\geq h>0\), and a growth condition with respect to \(\xi\). Here, \(\omega_i\), \(\omega_i^\ast\) are weight functions that will be defined in the Preliminaries.
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 6529022
zbMATH Keywords: degenerate elliptic problems
zbMATH Keywords: weighted Sobolev space
Wikidata QID: Q59112783
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/265127
OpenAlex ID: W2260042741
cites work: Pseudo-monotonicity and degenerated or singular elliptic operators
cites work: Existence of solutions for quasilinear degenerate elliptic equations
cites work: Renormalized solutions of degenerate elliptic problems
cites work: Quasilinear degenerated equations with L 1 datum and without coercivity in perturbation terms
cites work: Weighted Sobolev spaces and embedding theorems
cites work: Existence and nonexistence of solutions for some nonlinear elliptic equations
cites work: Existence of renormalized solutions to a nonlinear parabolic equation in L1 setting with nonstandard growth condition and gradient term
cites work: On a nonlinear partial differential equation having natural growth terms and unbounded solution
cites work: Q4219711
cites work: Semi-linear second-order elliptic equations in \(L^1\)
description: scientific article; zbMATH DE number 6529022