Local and Nonlocal Singular Liouville Equations in Euclidean Spaces

被引：17

作者：

Hyder, Ali ^{[1
]}

Mancini, Gabriele ^{[2
]}

Martinazzi, Luca ^{[3
]}

机构：

[1] Johns Hopkins Univ, Baltimore, MD 21218 USA

[2] Univ Sapienza Roma, I-00185 Rome, Italy

[3] Univ Padua, I-35121 Padua, Italy

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2021年 / 2021卷 / 15期

基金：

瑞士国家科学基金会;

关键词：

Q-curvature; fractional Laplacian; conformal geometry; GJMS-operator; CONSTANT Q-CURVATURE; INVARIANT 4TH-ORDER EQUATION; CONFORMAL METRICS; R-N; CLASSIFICATION; R-2M; UNIQUENESS; SYMMETRY;

D O I：

10.1093/imrn/rnz149

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the metrics of constant Q-curvature in the Euclidean space with a prescribed singularity at the origin, namely solutions to the equation (-Delta)(n/2)w = e(nw) - c delta(0) on R-n, under a finite volume condition. We analyze the asymptotic behavior at infinity and the existence of solutions for every n = 3 also in a supercritical regime. Finally, we state some open problems.

引用

页码：11393 / 11425

页数：33

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[3]

Branson T., 1991, COMMUN PART DIFF EQ, V16, P1223, DOI DOI 10.1080/03605309108820797

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