A singular perturbation problem for the p-Laplace operator

被引：0
|
作者：
Danielli, D [1 ]
Petrosyan, A
Shahgholian, H
机构：
[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
[2] Univ Texas, Dept Math, Austin, TX 78712 USA
[3] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden
来源：
INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2003年 / 52卷 / 02期
关键词：
singular perturbation problem; free boundary problem; p-Laplace operator; uniform gradient bounds;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we initiate the study of the nonlinear one phase singular perturbation problem div(\delu(epsilon)\(p-2)delu(epsilon)) = beta(epsilon)(u(epsilon)), (1 < p < infinity) in a domain Omega of R-N. We prove uniform Lipschitz regularity of uniformly bounded solutions. Once this is done we can pass to the limit to obtain a solution to the stationary case of a combustion problem with a nonlinearity of power type. (The case p = 2 has been considered earlier by several authors.).
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收藏
页码：457 / 476
页数：20
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