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On a question of Brezis and Marcus

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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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Authors and Affiliations

  1. Department of Applied Mathematics, University of Crete, 71409, Heraklion, Greece

    S. Filippas

  2. Institute of Applied and Computational Mathematics, FORTH, 71110, Heraklion, Greece

    S. Filippas

  3. Department of Mathematical Sciences, The University of Liverpool, M&O Building, Peach Street, Liverpool, L69 72L, UK

    V. Maz'ya

  4. Department of Mathematics, Ohio State University Columbus, OH, 43210, USA

    V. Maz'ya

  5. Department of Mathematics, University of Crete, 71409, Heraklion, Greece

    A. Tertikas

  6. Institute of Applied and Computational Mathematics, FORTH, 71110, Heraklion, Greece

    A. Tertikas

Authors
  1. S. Filippas
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  2. V. Maz'ya
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  3. A. Tertikas
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Filippas, S., Maz'ya, V. & Tertikas, A. On a question of Brezis and Marcus. Calc. Var. 25, 491–501 (2006). https://doi.org/10.1007/s00526-005-0353-6

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  • DOI: https://doi.org/10.1007/s00526-005-0353-6

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