On the critical Neumann problem with weight in exterior domains.
type: Item
instance of: scholarly article
title: On the critical Neumann problem with weight in exterior domains.
zbMATH Open document ID: 1163.35370
DOI: 10.1016/S0362-546X(03)00059-2
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-06-17T00:00:00Z
review text: Let \(\Omega\subset\mathbb R^n\) be a bounded domain with a smooth boundary \(\partial\Omega\) and set \(\Omega^c=\mathbb R^N\setminus \overline{\Omega}\). Here, the authors study the nonlinear Neumann problem \[ -\Delta u+\lambda u= Q(x)|u|^{2^*-2}u \quad\text{in }\Omega^c,\quad u>0, \qquad \frac{\partial u}{\partial\nu}=0 \quad\text{on }\partial\Omega, \] where the coefficient \(Q\) is continuous and positive on \(\overline{\Omega}^c\), \(\lambda>0\) is a parameter and \(2^*= \frac {2N}{N-2}\), \(N\) is a critical Sobolev exponent. The authors study the common effect of the mean curvature for the boundary \(\partial\Omega\) and the shape of the graph of the coefficient \(Q\) on the existence of least energy solutions.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1929513
zbMATH Keywords: Neumann problem
zbMATH Keywords: exterior domains
zbMATH Keywords: critical Sobolev exponent
zbMATH Keywords: least energy
zbMATH Keywords: solutions
zbMATH Keywords: optimal Sobolev inequalities
Wikidata QID: Q59311003
author: Jan Chabrowski
author: Bernhard Ruf
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1929513