JournalsrlmVol. 30, No. 4pp. 665–676

A Sharp estimate for the first Robin–Laplacian eigenvalue with negative boundary parameter

  • Dorin Bucur

    Université Savoie Mont Blanc, Chambéry, France

  • Vincenzo Ferone

    Università degli Studi di Napoli Federico II, Italy

  • Carlo Nitsch

    Università degli Studi di Napoli Federico II, Italy

  • Cristina Trombetti

    Università degli Studi di Napoli Federico II, Italy
A Sharp estimate for the first Robin–Laplacian eigenvalue with negative boundary parameter cover

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Abstract

In this paper we prove that the ball maximizes the first eigenvalue of the Robin Laplacian operator with negative boundary parameter, among all convex sets of Rn with prescribed perimeter. The key of the proof is a dearrangement procedure of the first eigenfunction of the ball on the level sets of the distance function to the boundary of the convex set, which controls the boundary and the volume energies of the Rayleigh quotient.

Cite this article

Dorin Bucur, Vincenzo Ferone, Carlo Nitsch, Cristina Trombetti, A Sharp estimate for the first Robin–Laplacian eigenvalue with negative boundary parameter. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 4, pp. 665–676

DOI 10.4171/RLM/866