Borderline Variational Problems Involving Fractional Laplacians and Critical Singularities-Reference-Cited by-同舟云学术

Borderline Variational Problems Involving Fractional Laplacians and Critical Singularities

Published:2015-08-01 Issue:3 Volume:15 Page:527-555
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Ghoussoub Nassif¹,Shakerian Shaya¹

Affiliation:

1. Department of Mathematics University of British Columbia, Vancouver, B.C. Canada V6T 1Z2

Abstract

Abstract We consider the problem of attainability of the best constant C > 0 in the following critical fractional Hardy-Sobolev inequality: For all

, where

and γ ∈ ℝ. This allows us to establish the existence of nontrivial weak solutions for the following doubly critical problem on ℝn,

, where

is the critical α-fractional Sobolev exponent, and

, the latter being the best fractional Hardy constant on ℝn.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2015-0302/pdf

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