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Journal Articles Discrete and Continuous Dynamical Systems - Series B Year : 2014

Spectral minimal partitions of a sector

Abstract

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.
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Dates and versions

hal-00763467 , version 1 (10-12-2012)

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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⟩
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