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On the Hong–Krahn–Szego inequality for the p-Laplace operator

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Abstract

Given an open set Ω, we consider the problem of providing sharp lower bounds for λ 2(Ω), i.e. its second Dirichlet eigenvalue of the p-Laplace operator. After presenting the nonlinear analogue of the Hong–Krahn–Szego inequality, asserting that the disjoint unions of two equal balls minimize λ 2 among open sets of given measure, we improve this spectral inequality by means of a quantitative stability estimate. The extremal cases p = 1 and p = ∞ are considered as well.

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Authors and Affiliations

  1. Laboratoire d’Analyse, Topologie, Probabilités, Aix-Marseille Université, 39 Rue Frédéric Joliot Curie, 13453, Marseille Cedex 13, France

    Lorenzo Brasco

  2. Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38100, Povo, Trento, Italy

    Giovanni Franzina

Authors
  1. Lorenzo Brasco
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  2. Giovanni Franzina
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Correspondence to Lorenzo Brasco.

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Brasco, L., Franzina, G. On the Hong–Krahn–Szego inequality for the p-Laplace operator. manuscripta math. 141, 537–557 (2013). https://doi.org/10.1007/s00229-012-0582-x

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