涉及Sobolev临界指数和临界维数椭圆边值问题正解的存在性  

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

作　　者：饶若峰[1] 黄家琳[1] 

机构地区：[1]宜宾学院数学系,四川宜宾644000

出　　处：《吉林大学学报（理学版）》2008年第3期423-427,共5页Journal of Jilin University:Science Edition

基　　金：四川省教育厅重点项目基金(批准号:2005A175);宜宾学院课题基金

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).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.

关 键 词：SOBOLEV临界指数 非平凡强解 山路引理 强极值原理 

分 类 号：O175.25[理学—数学]