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Isoperimetric estimates for eigenfunctions of Hessian operators

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Abstract

In this paper we consider the eigenvalue problem for a fully nonlinear equation involving Hessian operators. In particular we study some properties of the first eigenvalue and of corresponding eigenfunctions. Using suitable symmetrization arguments, we prove a Faber–Krahn inequality for the first eigenvalue and a Payne–Rayner type inequality for eigenfunctions, which are well known for the p-laplacian operator and the Monge–Ampere operator.

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Authors and Affiliations

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

    Nunzia Gavitone

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  1. Nunzia Gavitone
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Correspondence to Nunzia Gavitone.

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Communicated by V. Ferone.

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Gavitone, N. Isoperimetric estimates for eigenfunctions of Hessian operators. Ricerche mat. 58, 163–183 (2009). https://doi.org/10.1007/s11587-009-0058-9

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