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1995 Characterization of concentration points and $L^\infty$-estimates for solutions of a semilinear Neumann problem involving the critical Sobolev exponent
Adimurthi, Filomena Pacella, S. L. Yadava
Differential Integral Equations 8(1): 41-68 (1995).

Abstract

$\Omega\subset\mathbb{R}^n(n\geq7)$ be a bounded domain with smooth boundary. For $\lambda>0$, let $u_\lambda$ be a solution of $$ \begin{align} -\Delta u+\lambda u&=u^{n+2\over n-2}\quad\rm{in }\quad\Omega,\\ u&>0\quad\rm{in }\quad\Omega,\\ {\partial u\over\partial\nu}&=0\quad\rm{on }\quad\partial\Omega, \end{align} $$ whose energy is less than the first critical level. Here we study the blow up points and the $L^\infty$-estimates of $u_\lambda$ as $\lambda\to\infty$. We show that the blow up points are the critical points of the mean curvature on the boundary.

Citation

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Adimurthi. Filomena Pacella. S. L. Yadava. "Characterization of concentration points and $L^\infty$-estimates for solutions of a semilinear Neumann problem involving the critical Sobolev exponent." Differential Integral Equations 8 (1) 41 - 68, 1995.

Information

Published: 1995
First available in Project Euclid: 21 May 2013

zbMATH: 0814.35029
MathSciNet: MR1296109

Subjects:
Primary: 35J65
Secondary: 35B40

Rights: Copyright © 1995 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.8 • No. 1 • 1995
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