Nodal domains and spectral minimal partitions

2006/10/31 by Bernard Helffer, B. Helffer, Helffer, B. +6 · 3 citations
Computer Science · Mathematics · #35J20 #35J99 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.AP #math.SP #msc:35J20 #msc:35J99

paper · pdf · doi:10.48550/arxiv.math/0610975

arxiv created 2006/10/31 · openalex publication_date 2006/10/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider two-dimensional Schrödinger operators in bounded domains. We analyze relations between nodal domains of eigenfunctions, spectral minimal partitions and spectral properties of the corresponding operator. The main results concern the existence and regularity of the minimal partitions associated with the nodal sets as the nodal domains of Courant-sharp eigenfunctions.

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• Spectral minimal partitions of unbounded domains
• Spectral flow and Robin domains on metric graphs

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