Best Sobolev constants in the presence of sharp Hardy terms in Euclidean and hyperbolic space

Abstract

In this article we compute the best Sobolev constants for various Hardy-Sobolev inequalities with sharp Hardy term. This is carried out in three different environments: interior point singularity in Euclidean space, interior point singularity in hyperbolic space and boundary point singularity in Euclidean domains.

27 pages

References in corpus (1)

• Hardy-Sobolev-Maz'ya inequalities for higher order derivatives on half spaces