# Minimization of $λ_2(Ω)$ with a perimeter constraint

Bucur, Dorin and Buttazzo, Giuseppe and Henrot, Antoine (2009) Minimization of $λ_2(Ω)$ with a perimeter constraint. Indiana University mathematics journal, 58 (6). pp. 2709-2728. ISSN 1943-5258

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## Abstract

We study the problem of minimizing the second Dirichlet eigenvalue for the Laplacian operator among sets of given perimeter. In two dimensions, we prove that the optimum exists, is convex, regular, and its boundary contains exactly two points where the curvature vanishes. In $N$ dimensions, we prove a more general existence theorem for a class of functionals which is decreasing with respect to set inclusion and $\gamma$ lower semicontinuous.

Item Type: Article Imported from arXiv Area01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica Dipartimenti (from 2013) > DIPARTIMENTO DI MATEMATICA dott.ssa Sandra Faita 05 Aug 2013 12:48 05 Aug 2013 12:48 http://eprints.adm.unipi.it/id/eprint/1341

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