Qualitative and Numerical Analysis of a Spectral Problem with Perimeter Constraint | Zendy

Beniamin Bogosel | Zendy; Èdouard Oudet | Zendy

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Qualitative and Numerical Analysis of a Spectral Problem with Perimeter Constraint

Author(s) -

Beniamin Bogosel,

Èdouard Oudet

Publication year - 2016

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/140999530

Subject(s) - perimeter , eigenvalues and eigenvectors , constraint (computer aided design) , mathematics , convergence (economics) , laplace operator , operator (biology) , laplace transform , mathematical optimization , mathematical analysis , geometry , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , economics , gene , economic growth

We consider the problem of optimizing the $k{\text{th}}$ eigenvalue of the Dirichlet Laplace operator under perimeter constraint. We provide a new method based on a $\Gamma$-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.

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