Elliptic equations with critical Sobolev exponents in dimension 3
type: Item
instance of: scholarly article
title: Elliptic equations with critical Sobolev exponents in dimension 3
zbMATH Open document ID: 1011.35060
DOI: 10.1016/S0294-1449(02)00095-1
author: Olivier Druet
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2003-06-04T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78541
review text: The author studies the following problem: \[ \begin{cases} \Delta u+au= u^{2^*-1} \quad &\text{in }\Omega\\ u>0\quad &\text{in }\Omega\\ u=0\quad &\text{on }\partial \Omega,\end{cases} \tag{1} \] where \(a\) is smooth function in \(\Omega\), \(2^*={2n \over n-2}\) is critical for the embeddings of \(H^1_0(\Omega)\) into \(L^q(\Omega)\), and \(\Omega\) is a smooth bounded domain of \(\mathbb{R}^n\), \(n\geq 3\). He is mainly interested in the existence of minimizing solutions for an elliptic equation of the form (1).
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B33
zbMATH DE Number: 1785826
zbMATH Keywords: minimizing solution
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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OpenAlex ID: W2001158391
description: scientific article; zbMATH DE number 1785826