Optimal partitions for eigenvalues

Blaise Bourdain (1) , Dorin Bucur (2) , Edouard Oudet (2, 3)

1 Department of Mathematics Louisiana State University
2 LAMA - Laboratoire de Mathématiques
3 Département de mathématiques

We introduce a new numerical method to approximate partitions of a domain minimizing the sum of Dirichlet- Laplacian eigenvalues of any order. First we prove the equivalence of the original problem and a relaxed formulation based on measures. Using this result, we build a numerical algorithm to approximate optimal configurations. We describe numerical experiments aimed at studying the asymptotic behavior of optimal partitions with large numbers of cells.

Domaines: Equations aux dérivées partielles [math.AP]

Blaise Bourdain, Dorin Bucur, Edouard Oudet. Optimal partitions for eigenvalues. 2009. ⟨hal-00385170⟩