Some remarks on convex combinations of low eigenvalues

Dario Cesare Severo Mazzoleni

Some remarks on convex combinations of low eigenvalues

Dario Cesare Severo Mazzoleni^*

^*Autore corrispondente per questo lavoro

Università Cattolica del Sacro Cuore

Risultato della ricerca: Contributo in rivista › Contributo a convegno › peer 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 originale	English
pagine (da-a)	43-52
Numero di pagine	10
Rivista	Rendiconti del Seminario Matematico
Volume	74
Stato di pubblicazione	Pubblicato - 2016
Evento	Bruxelles-Turin talks in PDEs - Torino Durata: 2 mag 2016 → 5 mag 2016

Keywords

Mathematics (all)

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AB - 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.

KW - Mathematics (all)

UR - http://hdl.handle.net/10807/117120

UR - http://seminariomatematico.dm.unito.it/rendiconti/64-1.html

M3 - Conference article

SN - 0373-1243

VL - 74

SP - 43

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JO - Rendiconti del Seminario Matematico

JF - Rendiconti del Seminario Matematico

T2 - Bruxelles-Turin talks in PDEs

Y2 - 2 May 2016 through 5 May 2016

ER -

Some remarks on convex combinations of low eigenvalues

Abstract

Keywords

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