The Neumann problem for semilinear elliptic equations with critical Sobolev exponent
type: Item
instance of: scholarly article
title: The Neumann problem for semilinear elliptic equations with critical Sobolev exponent
zbMATH Open document ID: 1139.35316
published in: Milan Journal of Mathematics
publication date: 2008-06-24T00:00:00Z
review text: This paper is mainly devoted to the study of least energy solutions of a nonlinear elliptic equation with critical Sobolev exponent and Neumann boundary condition. The existence of solutions is deduced with topological linking arguments combined with sharp Sobolev inequalities. This result is then extended to singular potentials by means of the Hardy-Sobolev inequality. Related regularity properties of solutions are also established in the present paper.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 5292360
zbMATH Keywords: Critical Sobolev exponent
zbMATH Keywords: Hardy-Sobolev potential
zbMATH Keywords: Concentration-compactness principle
zbMATH Keywords: Least energy solutions
zbMATH Keywords: Weighted Sobolev inequalities
author: Jan Chabrowski
MaRDI profile type: Publication
full work available at URL: s00032-006-0065-1
OpenAlex ID: W2026174561
DOI: 10.1007/S00032-006-0065-1
description: scientific article; zbMATH DE number 5292360