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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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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
Additional Information: Imported from arXiv
Subjects: Area01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica
Divisions: Dipartimenti (from 2013) > DIPARTIMENTO DI MATEMATICA
Depositing User: dott.ssa Sandra Faita
Date Deposited: 05 Aug 2013 12:48
Last Modified: 05 Aug 2013 12:48
URI: http://eprints.adm.unipi.it/id/eprint/1341

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