On a nonlinear elliptic equation arising in a free boundary problem

被引：12
|
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.
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页码：531 / 548
页数：18
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