SHARP CONSTANT AND EXTREMAL FUNCTION FOR THE IMPROVED MOSER-TRUDINGER INEQUALITY INVOLVING L-p NORM IN TWO DIMENSION

Lu GZ; Yang YY

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SHARP CONSTANT AND EXTREMAL FUNCTION FOR THE IMPROVED MOSER-TRUDINGER INEQUALITY INVOLVING L-p NORM IN TWO DIMENSION

机译：SHARP CONSTANT AND EXTREMAL FUNCTION FOR THE IMPROVED MOSER-TRUDINGER INEQUALITY INVOLVING L-p NORM IN TWO DIMENSION

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摘要

Let Omega subset of R-2 be a smooth bounded domain, and H-0(1)(Omega) be the standard Sobolev space. Define for any p > 1, lambda(p)(Omega)= inf(u is an element of H01(Omega), u not equivalent to 0) parallel to del u parallel to(2)(2)/parallel to u parallel to(2)(p), where parallel to center dot parallel to(p) denotes L-p norm. We derive in this paper a sharp form of the following improved Moser-Trudinger inequality involving the L-p-norm using the method of blow-up analysis: sup(u is an element of H01(Omega),parallel to del u parallel to 2=1)integral(Omega) (e4 pi(1+alpha parallel to u parallel to p2)u2) dx = lambda(p)(Omega). We also prove the existence of the extremal functions for this inequality when alpha is sufficiently small.

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来源
《Discrete and continuous dynamical systems》 |2009年第3期|963-979|共17页
作者
Lu GZ; Yang YY;
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作者单位

Wayne State Univ, Dept Math, Detroit, MI 48202 USA.;

Renmin Univ China, Informat Sch, Dept Math, Beijing 100872, Peoples R China.;

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正文语种英语
中图分类理论力学（一般力学）;
关键词
Sharp constant; extremal function; Moser-Trudinger inequality; blow-up analysis; Euler-Lagrange equation; concentration-compactness;

SHARP CONSTANT AND EXTREMAL FUNCTION FOR THE IMPROVED MOSER-TRUDINGER INEQUALITY INVOLVING L-p NORM IN TWO DIMENSION

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