Hardy-Sobolev-Maz'ya type equations in bounded domains

被引：24

作者：

Bhakta, M. ^{[1
]}

Sandeep, K. ^{[1
]}

机构：

[1] TIFR Ctr Applicable Math, Bangalore 560065, Karnataka, India

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 247卷 / 01期

关键词：

GLOBAL COMPACTNESS RESULT; HYPERBOLIC SYMMETRY; ELLIPTIC-EQUATIONS; NONLINEARITIES; EXISTENCE;

D O I：

10.1016/j.jde.2008.12.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the regularity, Palais-Smale characterization and existence/nonexistence of solutions of the Hardy-Sobolev-Maz'ya equation -Delta u - lambda u/vertical bar y vertical bar(2) = vertical bar u vertical bar(pt-1) u/vertical bar y vertical bar(t) in a bounded domain in R-N where x is an element of R-N is denoted as x = (y, z) is an element of R-k x RN-k and P-t = N+2-2t/N-2 . we show different behaviors of PS sequences depending on t = 0 or t > 0. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：119 / 139

页数：21

共 16 条

[1]

CAO D, METHODS APP IN PRESS

[2] Solutions to critical elliptic equations with multi-singular inverse square potentials [J].

Cao, DM ;

Han, PG .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 224 (02) :332-372

[3] A global compactness result for singular elliptic problems involving critical Sobolev exponent [J].

Cao, DM ;

Peng, SJ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (06) :1857-1866

[4] Solutions for semilinear elliptic equations with critical exponents and Hardy potential [J].

Cao, DM ;

Han, PG .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 205 (02) :521-537

[5]

CARON JM, 1984, C R ACAD SCI PARIS 1, V299, P209

[6]

Castorina D, 2008, REND LINCEI-MAT APPL, V19, P189

[7] Hardy-Sobolev extremals, hyperbolic symmetry and scalar curvature equations [J].

Castorina, D. ;

Fabbri, I. ;

Mancini, G. ;

Sandeep, K. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (03) :1187-1206

[8] Classification of solutions of a critical Hardy-Sobolev operator [J].

Mancini, G. ;

Fabbri, I. ;

Sandeep, K. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 224 (02) :258-276

[9]

MANCINI G, ANN SC NO S IN PRESS

[10]

MAZ'JA V. G., 1985, SPRINGER SER SOVIET

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