6533b855fe1ef96bd12b15f9

RESEARCH PRODUCT

In between the inequalities of Sobolev and Hardy

Juha LehrbäckAntti Vähäkangas

subject

Mathematics::Functional AnalysisEuclidean spaceHardy-Sobolev inequalities

description

We establish both sufficient and necessary conditions for the validity of the so-called Hardy–Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev inequalities and the (weighted) Hardy inequalities. The Assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions. peerReviewed

yearjournalcountryeditionlanguage
2016-01-01
http://urn.fi/URN:NBN:fi:jyu-201906253431