6533b862fe1ef96bd12c6d97

RESEARCH PRODUCT

In between the inequalities of Sobolev and Hardy

Juha LehrbäckAntti V. VähäkangasAntti V. Vähäkangas

subject

Pure mathematicsInequalitymedia_common.quotation_subjectDimension (graph theory)Open set35A23 (26D15 46E35)Scale (descriptive set theory)01 natural sciencesSobolev inequalityMathematics - Analysis of PDEsEuclidean spaceClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsmedia_commonComplement (set theory)MathematicsMathematics::Functional AnalysisEuclidean space010102 general mathematicsMathematical analysista111010101 applied mathematicsSobolev spaceMathematics - Classical Analysis and ODEsHardy-Sobolev inequalitiesAnalysisAnalysis of PDEs (math.AP)

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.

yearjournalcountryeditionlanguage
2015-02-04
https://dx.doi.org/10.48550/arxiv.1502.01190