Qualitative and Numerical Analysis of a Spectral Problem with Perimeter Constraint

Abstract : We consider the problem of optimizing the k th 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.
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

http://hal.univ-grenoble-alpes.fr/hal-02009510
Contributor : Edouard Oudet <>
Submitted on : Wednesday, February 20, 2019 - 10:21:16 AM
Last modification on : Thursday, July 11, 2019 - 11:44:01 AM
Long-term archiving on : Tuesday, May 21, 2019 - 12:57:34 PM

File

gamma-conv-perim (1).pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Beniamin Bogosel, Edouard Oudet. Qualitative and Numerical Analysis of a Spectral Problem with Perimeter Constraint. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, 54 (1), pp.317-340. ⟨10.1137/140999530⟩. ⟨hal-02009510⟩

Share

Metrics

Record views

108

Files downloads

155