On a nonlinear elliptic equation arising in a free boundary problem

被引：13

作者：

Wang, GF

Ye, D

机构：

[1] Max Planck Inst Math, D-04103 Leipzig, Germany

[2] Univ Cergy Pontoise, Dept Math, F-95302 Cergy Pontoise, France

[3] ENS Cachan, CMLA, F-94235 Cachan, France

来源：

MATHEMATISCHE ZEITSCHRIFT | 2003年 / 244卷 / 03期

关键词：

D O I：

10.1007/s00209-003-0493-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p* = n/(n - 2) and n greater than or equal to 3. In this paper, we first classify all non-constant solutions of [GRAPHICS] We then establish a sup + inf and a Moser-Trudinger type inequalities for the equation -Deltau = u(+)(p)*. Our results illustrate that this equation is much closer to the Liouville problem -Deltau = e(u) in dimension two than the usual critical exponent equation, namely -DeltaU = Un+2/n-2 is.

引用

页码：531 / 548

页数：18

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