FRACTIONAL CONFORMAL LAPLACIANS AND FRACTIONAL YAMABE PROBLEMS

被引：87

作者：

del Mar Gonzalez, Maria ^{[1
]}

Qing, Jie ^{[2
]}

机构：

[1] Univ Politecn Cataluna, ETSEIB, Dept Matemat Aplicada 1, E-08028 Barcelona, Spain

[2] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

来源：

ANALYSIS & PDE | 2013年 / 6卷 / 07期

基金：

美国国家科学基金会;

关键词：

fractional Laplacian; conformal geometry; Yamabe problem; SOBOLEV INEQUALITIES; SHARP INEQUALITIES; REGULARITY; DIFFUSION; CONSTANTS; EQUATION; EXTENSION; CURVATURE;

D O I：

10.2140/apde.2013.6.1535

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems observed by Chang and Gonzalez, we formulate fractional Yamabe problems that include the boundary Yamabe problem studied by Escobar. We observe an interesting Hopf-type maximum principle together with interplay between analysis of weighted trace Sobolev inequalities and conformal structure of the underlying manifolds, which extends the phenomena displayed in the classic Yamabe problem and boundary Yamabe problem.

引用

页码：1535 / 1576

页数：42