Search results for "Rearrangement inequality"

showing 2 items of 2 documents

Hardy’s inequality and the boundary size

2002

We establish a self-improving property of the Hardy inequality and an estimate on the size of the boundary of a domain supporting a Hardy inequality.

Hölder's inequalityKantorovich inequalityMathematics::Functional AnalysisPure mathematicsInequalityMathematics::Complex VariablesApplied MathematicsGeneral Mathematicsmedia_common.quotation_subjectMathematical analysisMathematics::Classical Analysis and ODEsBoundary (topology)Mathematics::Spectral TheoryLog sum inequalityRearrangement inequalityCauchy–Schwarz inequalityHardy's inequalityMathematicsmedia_commonProceedings of the American Mathematical Society
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On improved fractional Sobolev–Poincaré inequalities

2016

We study a certain improved fractional Sobolev–Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev–Poincaré inequality. We prove the equivalence of the corresponding weak and strong type inequalities; this leads to a simple proof of a strong type inequality on John domains. We also give necessary conditions for the validity of an improved fractional Sobolev–Poincaré inequality, in particular, we show that a domain of finite measure, satisfying this inequality and a ‘separation property’, is a John domain.

Hölder's inequalityKantorovich inequalityPure mathematicsYoung's inequalityBernoulli's inequalityGeneral Mathematics010102 general mathematicsMathematical analysisMinkowski inequality01 natural sciences010101 applied mathematicsLog sum inequalityRearrangement inequality0101 mathematicsCauchy–Schwarz inequalityMathematicsArkiv för Matematik
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