涉及Sobolev临界指数和临界维数椭圆边值问题正解的存在性

涉及Sobolev临界指数和临界维数椭圆边值问题正解的存在性

饶若峰，黄家琳

宜宾学院数学系, 四川宜宾 644000

收稿日期:2007-06-04 修回日期:1900-01-01 出版日期:2008-05-26 发布日期:2008-05-26
通讯作者: 饶若峰

Existence of Positive Solution for Elliptic Boundary Value Problemwith Critical Sobolev Exponent and Critical Dimension

RAO Ruofeng, HUANG Jia lin

Department of Mathematics, Yibin College, Yibin 644000, Sichuan Province, China

Received:2007-06-04 Revised:1900-01-01 Online:2008-05-26 Published:2008-05-26
Contact: RAO Ruofeng

摘要/Abstract

摘要： 利用山路引理和强极值原理证明了一类具Sobolev临界指数Dirichlet问题正强解的存在性, 将Brezis和Nirenberg的相关结果延拓到该椭圆边值问题的临界维数空间(三维空间).

关键词: Sobolev临界指数, 非平凡强解, 山路引理, 强极值原理

Abstract: An existence theorem of positive strong solution for a Dirichlet problem with the critical Sobolev exponent was given by way of MountainPass Lemma and Strong Minimum Principle, which extended the corresponding results obtained by Brezis and Nirenberg to a threedimension space, the critical dimension space for the Dirichlet problem.

Key words: critical Sobolev exponent, positive strong solution, mountainpass lemma, strong minimum principle

中图分类号:

O175.25

饶若峰，黄家琳. 涉及Sobolev临界指数和临界维数椭圆边值问题正解的存在性[J]. J4, 2008, 46(03): 423-427.

RAO Ruofeng, HUANG Jia lin. Existence of Positive Solution for Elliptic Boundary Value Problemwith Critical Sobolev Exponent and Critical Dimension[J]. J4, 2008, 46(03): 423-427.

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