On a variational degenerate elliptic problem
type: Item
instance of: scholarly article
title: On a variational degenerate elliptic problem
zbMATH Open document ID: 0960.35039
author: Paolo Caldiroli
author: Roberta Musina
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2001-05-01T00:00:00Z
review text: It is considered the following degenerate elliptic boundary value problem \[ \text{-div}(a(x)\bigtriangledown u)=f(x,u)\quad \text{in }\Omega, \qquad u=0 \quad \text{on }\partial\Omega, \] where \(f\) is a given regular function, \(\Omega\) is a bounded or unbounded domain in \(\mathbb R^n, n\geq 2,\) and \(a(x)\) is a measurable and nonnegative weight on \(\Omega\), which can have at most a finite number of (essential) zeroes. A weighted Sobolev inequality which generalizes a result by \textit{L. Caffarelli, R. Kohn} and \textit{L. Nirenberg} [Compos. Math. 53, 259-275 (1984; Zbl 0563.46024)] is established. The existence of nonnegative weak solutions for problems under consideration is proved via variational methods.
reviewed by: Dmitry V. Larin
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 1508201
zbMATH Keywords: degenerate elliptic problem
zbMATH Keywords: weighted Sobolev inequality
zbMATH Keywords: weight
zbMATH Keywords: nonnegative solution
zbMATH Keywords: existence
zbMATH Keywords: variational method
MaRDI profile type: Publication
full work available at URL: s000300050004
OpenAlex ID: W2068862035
DOI: 10.1007/S000300050004
description: scientific article; zbMATH DE number 1508201