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

被引：36

作者：

Chen, Hua ^{[3
]}

Liu, Xiaochun ^{[3
]}

Wei, Yawei ^{[1
,2
]}

机构：

[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2012年 / 252卷 / 07期

关键词：

Dirichlet problem; Edge-degenerate elliptic operators; Singular potentials; Edge Sobolev inequality; Edge Hardy inequality;

D O I：

10.1016/j.jde.2012.01.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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, Poincare 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. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：4289 / 4314

页数：26

共 11 条

[1]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[2]

[Anonymous], 1991, COMMUNICATIONS PARTI

[3]

[Anonymous], 1986, CBMS REG C SER MATH

[4] Cone Sobolev inequality and Dirichlet problem for nonlinear elliptic equations on a manifold with conical singularities [J].

Chen, Hua ;

Liu, Xiaochun ;

Wei, Yawei .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2012, 43 (3-4) :463-484

[5] Existence theorem for a class of semilinear totally characteristic elliptic equations with critical cone Sobolev exponents [J].

Chen, Hua ;

Liu, Xiaochun ;

Wei, Yawei .

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2011, 39 (01) :27-43

[6]

Egorov Ju. V., 1997, OPER THEORY ADV APPL, V93

[7]

Hajlasz P, 2000, MEM AM MATH SOC, V145, pIX

[8]

Melrose R.B, 1983, 04783 MSRI

[9] SEMI-LINEAR SUB-ELLIPTIC EQUATIONS ON THE HEISENBERG GROUP WITH A SINGULAR POTENTIAL [J].

Mokrani, Houda .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (05) :1619-1636

[10] Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces [J].

Schrohe, E ;

Seiler, J .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2001, 41 (01) :93-114

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