6533b830fe1ef96bd12966fd

RESEARCH PRODUCT

Fractional Hardy inequalities and visibility of the boundary

Juha LehrbäckHeli TuominenLizaveta IhnatsyevaAntti V. Vähäkangas

subject

visibility of the boundaryPure mathematicsMathematics::Functional AnalysisInequalityfractional Hardy inequalitiesGeneral Mathematicsmedia_common.quotation_subject010102 general mathematicsVisibility (geometry)46E35 (26D15)Open setMathematics::Classical Analysis and ODEsOrder (ring theory)Boundary (topology)01 natural sciences010101 applied mathematicsMathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMathematicsExposition (narrative)media_common

description

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.

yearjournalcountryeditionlanguage
2013-05-20
10.4064/sm224-1-3http://arxiv.org/abs/1305.4616