Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem

Barbara Brandolini, Barbara Brandolini, Carlo Nitsch, Cristina Trombetti, Freitas

Risultato della ricerca: Articlepeer review

10 Citazioni (Scopus)

Abstract

We determine the shape which minimizes, among domains with given measure, the first eigenvalue of a nonlocal operator consisting of a perturbation of the standard Dirichlet Laplacian by an integral of the unknown function. We show that this problem displays a saturation behaviour in that the corresponding value of the minimal eigenvalue increases with the weight affecting the average up to a (finite) critical value of this weight, and then remains constant. This critical point corresponds to a transition between optimal shapes, from one ball as in the Faber-Krahn inequality to two equal balls.
Lingua originaleEnglish
pagine (da-a)2352-2365
Numero di pagine14
RivistaAdvances in Mathematics
Volume228
Stato di pubblicazionePublished - 2011

All Science Journal Classification (ASJC) codes

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