Qualitative and numerical analysis of a spectral problem with perimeter constraint

Beniamin Bogosel; Édouard Oudet

doi:10.1137/140999530

Qualitative and numerical analysis of a spectral problem with perimeter constraint

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the problem of optimizing the kth eigenvalue of the Dirichlet Laplace operator under perimeter constraint. We provide a new method based on a Γ-convergence result for approximating the corresponding optimal shapes. We also give new optimality conditions in the case of multiple eigenvalues. We deduce from previous conditions the fact that optimal shapes never contain flat parts in their boundaries.

Original language	English
Pages (from-to)	317-340
Number of pages	24
Journal	SIAM Journal on Control and Optimization
Volume	54
Issue number	1
DOIs	https://doi.org/10.1137/140999530
Publication status	Published - 1 Jan 2016
Externally published	Yes

Keywords

Eigenvalues
Gamma convergence
Optimality conditions
Shape optimization

Access to Document

10.1137/140999530

Cite this

@article{e512919879fc40a79b4fcfb37469552e,

title = "Qualitative and numerical analysis of a spectral problem with perimeter constraint",

abstract = "We consider the problem of optimizing the kth eigenvalue of the Dirichlet Laplace operator under perimeter constraint. We provide a new method based on a Γ-convergence result for approximating the corresponding optimal shapes. We also give new optimality conditions in the case of multiple eigenvalues. We deduce from previous conditions the fact that optimal shapes never contain flat parts in their boundaries.",

keywords = "Eigenvalues, Gamma convergence, Optimality conditions, Shape optimization",

author = "Beniamin Bogosel and {\'E}douard Oudet",

note = "Publisher Copyright: Copyright {\textcopyright} 2016 Society for Industrial and Applied Mathematics.",

year = "2016",

month = jan,

day = "1",

doi = "10.1137/140999530",

language = "English",

volume = "54",

pages = "317--340",

journal = "SIAM Journal on Control and Optimization",

issn = "0363-0129",

number = "1",

}

TY - JOUR

T1 - Qualitative and numerical analysis of a spectral problem with perimeter constraint

AU - Bogosel, Beniamin

AU - Oudet, Édouard

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We consider the problem of optimizing the kth eigenvalue of the Dirichlet Laplace operator under perimeter constraint. We provide a new method based on a Γ-convergence result for approximating the corresponding optimal shapes. We also give new optimality conditions in the case of multiple eigenvalues. We deduce from previous conditions the fact that optimal shapes never contain flat parts in their boundaries.

AB - We consider the problem of optimizing the kth eigenvalue of the Dirichlet Laplace operator under perimeter constraint. We provide a new method based on a Γ-convergence result for approximating the corresponding optimal shapes. We also give new optimality conditions in the case of multiple eigenvalues. We deduce from previous conditions the fact that optimal shapes never contain flat parts in their boundaries.

KW - Eigenvalues

KW - Gamma convergence

KW - Optimality conditions

KW - Shape optimization

U2 - 10.1137/140999530

DO - 10.1137/140999530

M3 - Article

AN - SCOPUS:84959931357

SN - 0363-0129

VL - 54

SP - 317

EP - 340

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 1

ER -

Qualitative and numerical analysis of a spectral problem with perimeter constraint

Abstract

Keywords

Access to Document

Fingerprint

Cite this