Existence of minimizers for spectral problems

Dario Cesare Severo Mazzoleni; Aldo Pratelli

doi:10.1016/j.matpur.2013.01.008

Existence of minimizers for spectral problems

Dario Cesare Severo Mazzoleni
, Aldo Pratelli

Università Cattolica del Sacro Cuore

Friedrich-Alexander University Erlangen-Nürnberg

Risultato della ricerca: Contributo in rivista › Articolo › peer review

51 Citazioni (Scopus)

Abstract

In this paper we show that any increasing functional of the first k eigenvalues of the Dirichlet Laplacian admits a (quasi-)open minimizer among the subsets of R^N of unit measure. In particular, there exists such a minimizer which is bounded, where the bound depends on k and N, but not on the functional.

Lingua originale	Inglese
pagine (da-a)	433-453
Numero di pagine	21
Rivista	JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES
Volume	100
DOI	https://doi.org/10.1016/j.matpur.2013.01.008
Stato di pubblicazione	Pubblicato - 2013

Keywords

Applied Mathematics
Dirichlet Laplacian
Eigenvalue problems
Mathematics (all)
Minimization of spectral functionals
Shape optimization

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10.1016/j.matpur.2013.01.008

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keywords = "Applied Mathematics, Dirichlet Laplacian, Eigenvalue problems, Mathematics (all), Minimization of spectral functionals, Shape optimization, Applied Mathematics, Dirichlet Laplacian, Eigenvalue problems, Mathematics (all), Minimization of spectral functionals, Shape optimization",

author = "Mazzoleni, \{Dario Cesare Severo\} and Aldo Pratelli",

year = "2013",

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AU - Pratelli, Aldo

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KW - Applied Mathematics

KW - Dirichlet Laplacian

KW - Eigenvalue problems

KW - Mathematics (all)

KW - Minimization of spectral functionals

KW - Shape optimization

KW - Applied Mathematics

KW - Dirichlet Laplacian

KW - Eigenvalue problems

KW - Mathematics (all)

KW - Minimization of spectral functionals

KW - Shape optimization

UR - http://hdl.handle.net/10807/118947

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JO - JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES

JF - JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES

ER -

Existence of minimizers for spectral problems

Abstract

Keywords

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