Search results for "visibility of the boundary"

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Fractional Hardy inequalities and visibility of the boundary

2013

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.

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
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