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An upper bound for nonlinear eigenvalues on convex domains by means of the isoperimetric deficit

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Abstract

We prove an upper bound for the first Dirichlet eigenvalue of the p-Laplacian operator on convex domains. The result implies a sharp inequality where, for any convex set, the Faber-Krahn deficit is dominated by the isoperimetric deficit.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, via Cintia, 80126, Naples, Italy

    Barbara Brandolini, Carlo Nitsch & Cristina Trombetti

Authors
  1. Barbara Brandolini
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  2. Carlo Nitsch
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  3. Cristina Trombetti
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Correspondence to Cristina Trombetti.

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Brandolini, B., Nitsch, C. & Trombetti, C. An upper bound for nonlinear eigenvalues on convex domains by means of the isoperimetric deficit. Arch. Math. 94, 391–400 (2010). https://doi.org/10.1007/s00013-010-0102-8

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  • DOI: https://doi.org/10.1007/s00013-010-0102-8

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