Dirichlet problems on varying domains

被引：71
作者：
Daners, D [1 ]
机构：
[1] Univ Sydney, Sch Math & Stat F07, Sydney, NSW 2006, Australia
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2003年 / 188卷 / 02期
关键词：
boundary value problems for second-order elliptic equations; domain convergence; singular perturbation of domain;
D O I：
10.1016/S0022-0396(02)00105-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The aim of the paper is to characterise sequences of domains for which solutions to an elliptic equation with Dirichlet boundary conditions converge to a solution of the corresponding problem on a limit domain. Necessary and sufficient conditions are discussed for strong and uniform convergence for the corresponding resolvent operators. Examples are given to illustrate that most results are optimal. (C) 2002 Elsevier Science (USA). All rights reserved.
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页码：591 / 624
页数：34
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