Some remarks on convex combinations of low eigenvalues

Dario Cesare Severo Mazzoleni

Some remarks on convex combinations of low eigenvalues

Dario Cesare Severo Mazzoleni^*

^*Corresponding author

Università Cattolica del Sacro Cuore

Research output: Contribution to journal › Conference article › 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.

Original language	English
Pages (from-to)	43-52
Number of pages	10
Journal	Rendiconti del Seminario Matematico
Volume	74
Publication status	Published - 2016
Event	Bruxelles-Turin talks in PDEs - Torino Duration: 2 May 2016 → 5 May 2016

Keywords

Mathematics (all)

Cite this

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title = "Some remarks on convex combinations of low eigenvalues",

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.",

keywords = "Mathematics (all), Mathematics (all)",

author = "Mazzoleni, \{Dario Cesare Severo\}",

year = "2016",

language = "English",

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journal = "Rendiconti del Seminario Matematico",

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note = "Bruxelles-Turin talks in PDEs ; Conference date: 02-05-2016 Through 05-05-2016",

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T1 - Some remarks on convex combinations of low eigenvalues

AU - Mazzoleni, Dario Cesare Severo

PY - 2016

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N2 - 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.

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

EP - 52

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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