Nodal and spectral minimal partitions -- The state of the art in 2015 --

Abstract

In this article, we propose a state of the art concerning the nodal and spectral minimal partitions. First we focus on the nodal partitions and give some examples of Courant sharp cases. Then we are interested in minimal spectral partitions. Using the link with the Courant sharp situation, we can determine the minimal k-partitions for some particular domains. We also recall some results about the topology of regular partitions and Aharonov-Bohm approach. The last section deals with the asymptotic behavior of minimal k-partition.

Cited by in corpus (5)

• Courant-sharp eigenvalues for the equilateral torus, and for the equilateral triangle
• Large $m$ asymptotics for minimal partitions of the Dirichlet eigenvalue
• Courant-sharp eigenvalues of Neumann 2-rep-tiles
• Stability of spectral partitions and the Dirichlet-to-Neumann map
• Computing nodal deficiency with a refined Dirichlet-to-Neumann map