Spectral minimal partitions of a sector

Virginie Bonnaillie-Noël (1) , Corentin Léna (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

In this article, we are interested in determining the spectral minimal $k$-partition for angular sectors. We first deal with the nodal cases for which we can determine explicitly the minimal partitions. Then, in the case where the minimal partitions are not given by eigenfunctions of the Dirichlet Laplacian, we analyze the possible topologies of the minimal partitions. We first exhibit symmetric minimal partitions by using mixed Dirichlet-Neumann Laplacian and then use a double covering approach to catch non symmetric candidates.

Mots clés: Spectral theory; minimal partitions; nodal domains; Aharonov-Bohm Hamiltonian; numerical simulations; finite element method

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Virginie Bonnaillie-Noël, Corentin Léna. Spectral minimal partitions of a sector. Discrete and Continuous Dynamical Systems - Series B, 2014, 19 (1), pp.27-53. ⟨10.3934/dcdsb.2014.19.27⟩. ⟨hal-00763467⟩