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arXiv · 1307.3788

On a conjectured reverse Faber-Krahn inequality for a Steklov-type Laplacian eigenvalue

Vincenzo Ferone·Carlo Nitsch·Cristina Trombetti
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Abstract

For a given bounded Lipschitz set $Ω$, we consider a Steklov--type eigenvalue problem for the Laplacian operator whose solutions provide extremal functions for the compact embedding $H^1(Ω)\hookrightarrow L^2(\partial Ω)$. We prove that a conjectured reverse Faber--Krahn inequality holds true at least in the class of Lipschitz sets which are "close" to a ball in a Hausdorff metric sense. The result implies that among sets of prescribed measure, balls are local minimizers of the embedding constant.

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Vincenzo Ferone, Carlo Nitsch, Cristina Trombetti. 2014-02-04. On a conjectured reverse Faber-Krahn inequality for a Steklov-type Laplacian eigenvalue. https://arxiv.org/abs/1307.3788

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