Some remarks on convex combinations of low eigenvalues

Dario Cesare Severo Mazzoleni

Risultato della ricerca: Contributo in rivistaContributo a convegnopeer review

Abstract

In this survey we deal with shape optimization problems involving convex combinations of the first two eigenvalues of the Dirichlet Laplacian, mainly recalling and explaining some recent results. More precisely, we discuss some geometric properties of minimizers, in particular when they are no longer convex and the optimality of balls. This leads us to deal with the "attainable set" of the first two eigenvalues, which is a great source of open problems.
Lingua originaleEnglish
pagine (da-a)43-52
Numero di pagine10
RivistaRendiconti del Seminario Matematico
Volume74
Stato di pubblicazionePubblicato - 2016
EventoBruxelles-Turin talks in PDEs - Torino
Durata: 2 mag 20165 mag 2016

Keywords

  • Mathematics (all)

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