Uniqueness of solutions for a mean field equation on torus

被引：27
作者：
Lin, Chang-Shou
Lucia, Marcello
机构：
[1] Natl Ctr Theoret Sci, Dept Math, Hsinchu, Taiwan
[2] Natl Chung Cheng Univ, Dept Math, Minghsiung, Chi Yi, Taiwan
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2006年 / 229卷 / 01期
关键词：
mean field equations; periodic solutions; uniqueness; isoperimetric profile;
D O I：
10.1016/j.jde.2005.11.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider on a two-dimensional flat torus T the following equation [GRAPHIC] When the fundamental domain of the torus is (0, a) x (0, b) (a >= b), we establish that the constants are the unique solutions whenever [GRAPHIC] and this result is sharp if b/a >=, pi/4. A similar conclusion is obtained for general two-dimensional torus by considering the length of the shortest closed geodesic. These results are derived by comparing the isoperimetric profile of the torus T with the one of the two-dimensional canonical sphere which has same volume as T. (c) 2005 Elsevier Inc. All rights reserved.
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页码：172 / 185
页数：14
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