A singular Moser-Trudinger embedding and its applications期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A singular Moser-Trudinger embedding and its applications

Authors:	Adimurthi K. Sandeep

Affiliation:	(1) TIFR Centre, IISc Campus, P.O. Box 1234, Bangalore, 560 012, India

Abstract:	Let Ω be a bounded domain in ${mathbb{R}}^{n}$ , we prove the singular Moser-Trudinger embedding: $mathop {suplimits_{parallel uparallel leqslant 1Omega } int {frac{{e^{alpha \|u\|^{frac{n} {{n - 1}}} } }}{{\|x\|^beta }}} } < infty$ if and only if $frac{alpha}{{alpha _n }} + frac{beta}{n} leqslant 1$ where $alpha > 0,beta in [0,n),u in W_0^{1,n} (Omega )$ and $parallel uparallel = left({intlimits_Omega {\|nabla u\|^n } } right)^frac{1}{n}$ . We will also study the corresponding critical exponent problem.

Keywords:	35B33 35J20 35J60
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