Defining the spectral position of a Neumann domain

DOI10.2140/apde.2023.16.2147zbMath1530.35163arXiv2009.14564OpenAlexW3091214061MaRDI QIDQ6145246

Sebastian K. Egger, Ram Band, Graham Cox

Publication date: 9 January 2024

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.14564

zbMATH Keywords

nodal domainsLaplacian eigenfunctionsMorse-Smale complexesNeumann domainsNeumann lines

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Elliptic equations on manifolds, general theory (58J05) Spectral theory; eigenvalue problems on manifolds (58C40) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Cites Work

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• Topological properties of Neumann domains
• The essential spectrum of Neumann Laplacians on some bounded singular domains
• Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps
• Eigenfunctions and nodal sets
• The spectral position of Neumann domains on the torus
• Strong coupling asymptotics for \(\delta \)-interactions supported by curves with cusps
• A dynamical approach to semilinear elliptic equations
• Neumann nodal domains
• Neumann Domains on Graphs and Manifolds
• Generic Properties of Eigenfunctions

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