TITLE

Boundary blow-up for a Brezis-Peletier problem on a singular domain

AUTHOR(S)
Angela Pistoia; Olivier Rey
PUB. DATE
November 2003
SOURCE
Calculus of Variations & Partial Differential Equations;Nov2003, Vol. 18 Issue 3, p243
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let $\tilde{\Omega}\in\mathbb{R}^{N}$ , $N\geq 3$ , be a bounded domain as defined by Flucher, Garroni and M�ller [6], which has a singular point $\overline{x}\in\partial\tilde{\Omega}$ such that the Robin?s function achieves its infimum at $\overline{x}$ . Considering the elliptic problem $(P_{\varepsilon}): \ -\Delta u = u^{p-\varepsilon},\ u > 0$ in $\tilde{\Omega}$ ; u = 0 on $\partial\tilde{\Omega}$ , with p = ( N + 2)/( N-2), $\varepsilon > 0$ , and $u_{\varepsilon}$ a minimizing solution of $(P_{\varepsilon})$ , $u_{\varepsilon}$ concentrates at $\overline{x}$ as $\varepsilon$ goes to zero.
ACCESSION #
11353174

 

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