A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results - Calcul des Variations, Géométrie, Image Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2016

A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results

Beniamin Bogosel
Bozhidar Velichkov

Résumé

In this paper we consider the following multiphase shape optimization problem $\min\big\{\sum_{i=1}^h\lambda_1(\Omega_i)+\alpha|\Omega_i|:\ \Omega_i\ {open},\ \Omega_i\subset D, \Omega_i\cap\Omega_j=\emptyset\big\}$, where $\alpha>0$ is a given constant and $D\subset\mathbb{R}^2$ is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.

Dates et versions

hal-02014013 , version 1 (11-02-2019)

Identifiants

Citer

Beniamin Bogosel, Bozhidar Velichkov. A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results. SIAM Journal on Numerical Analysis, 2016, 54 (1), pp.210-241. ⟨10.1137/140976406⟩. ⟨hal-02014013⟩
14 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More