Translator Disclaimer
May/June 2012 On the Brezis-Nirenberg Problem in a Ball
Zhijie Chen, Wenming Zou
Differential Integral Equations 25(5/6): 527-542 (May/June 2012).

Abstract

We study the following Brezis-Nirenberg type critical exponent problem: $$ \begin{cases}-\Delta u = \lambda u^q+ u^{2^{\ast}-1}\,\,\,\hbox{in} \,\,B_R,\\ u > 0\,\,\,\hbox{in}\,\, B_R,\quad u=0 \,\,\,\hbox{on} \,\, \partial B_R,\end{cases} $$ where $B_R$ is a ball with radius $R$ in $\mathbb R^N(N\ge3)$, ${\lambda} > 0$, $1\le q < 2^\ast-1 $, and $2^{\ast}$ is the critical Sobolev exponent. We prove the uniqueness results of the least-energy solution when $3\leq N\leq 5 $ and $1\le q < 2^\ast-1 $. We give extremely accurate energy estimates of the least-energy solutions as $R\to 0$ for $N\ge 4$ and $q=1$.

Citation

Download Citation

Zhijie Chen. Wenming Zou. "On the Brezis-Nirenberg Problem in a Ball." Differential Integral Equations 25 (5/6) 527 - 542, May/June 2012.

Information

Published: May/June 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1265.35072
MathSciNet: MR2951739

Subjects:
Primary: 35J60, 35J91, 35J92, 58E30

Rights: Copyright © 2012 Khayyam Publishing, Inc.

JOURNAL ARTICLE
16 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.25 • No. 5/6 • May/June 2012
Back to Top