Optimal Partitions for Eigenvalues

We introduce a new numerical method for approximating partitions of a domain minimizing the sum of DirichletLaplacian 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.