On a question of Brezis and Marcus |
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| Authors: | S Filippas V Maz'ya A Tertikas |
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| Institution: | (1) Department of Applied Mathematics, University of Crete, 71409 Heraklion, Greece;(2) Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion, Greece;(3) Department of Mathematical Sciences, The University of Liverpool, M&O Building, Peach Street, Liverpool, L69 72L, UK;(4) Department of Mathematics, Ohio State University Columbus, OH 43210, USA;(5) Department of Mathematics, University of Crete, 71409 Heraklion, Greece;(6) Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion, Greece |
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| Abstract: | Motivated by a question of Brezis and Marcus, we show that the Lp–Hardy inequality involving the distance to the boundary of a convex domain, can be improved by adding an Lq norm q ≥ p, with a constant depending on the interior diameter of Ω. |
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| Keywords: | Hardy inequality Distance function Convexity Inner radius |
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