Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains

被引：20
作者：
Dancer, EN [1 ]
Zhang, KW
机构：
[1] Univ Sydney, Dept Math, Sydney, NSW 2006, Australia
[2] Macquarie Univ, Dept Math, Sydney, NSW 2109, Australia
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2000年 / 41卷 / 5-6期
基金：
澳大利亚研究理事会;
关键词：
nearly star-shaped; nonlinear elliptic equation;
D O I：
10.1016/S0362-546X(98)00307-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This study explores the stability of the uniqueness of the trivial solutions when a star-shaped domain is perturbed. For a general variational integral, the uniqueness result is obtained by establishing a Pohozaev identity. In the case of star-shaped domains, a simple vector field is used in the Pohozaev identity.
引用
收藏
页码：745 / 761
页数：17
相关论文
共 15 条
[1]  
Adams A, 2003, SOBOLEV SPACES
[2]  
[Anonymous], WEAKLY DIFFERENTIABL
[3]  
BALL JM, 1977, ARCH RATION MECH AN, V63, P337, DOI 10.1007/BF00279992
[4]  
Ball JM, 1977, Herriot Watt Symposion: Nonlinear Analysis and Mechanics, V1, P187
[5]   SOME CONSTANCY RESULTS FOR NEMATIC LIQUID-CRYSTALS AND HARMONIC MAPS [J].
CHOU, KS ;
ZHU, XP .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1995, 12 (01) :99-115
[6]  
COURANT R, 1953, METHOD MATH PHYSICS, V1
[7]  
Dacorogna B., 1989, DIRECT METHODS CALCU
[8]  
DANCER EN, UNPUB REMARKS PURE C
[9]  
EVANS LC, 1986, ARCH RATION MECH AN, V95, P227
[10]  
Gilbar D., 1983, ELLIPTIC PARTIAL DIF
12