Dirichlet problem for semilinear edge-degenerate elliptic equations with singular potential term

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• 作者：Hua Chen^a ; ^{chenhua@whu.edu.cn} ; Xiaochun Liu^a ; ^{xcliu@whu.edu.cn} ; Yawei Wei^b ; ^{weiyawei@nankai.edu.cn}
• 关键词：35J20 ; 58J05
• 刊名：Journal of Differential Equations
• 出版年：2012
• 出版时间：1 April 2012
• 年：2012
• 卷：252
• 期：7
• 页码：4289-4314
• 全文大小：292 K

文摘

In this paper, we introduce weighted p-Sobolev spaces on manifolds with edge singularities. We give the proof for the corresponding edge type Sobolev inequality, Poincar¨¦ inequality and Hardy inequality. As an application of these inequalities, we prove the existence of nontrivial weak solutions for the Dirichlet problem of semilinear elliptic equations with singular potentials on manifolds with edge singularities.