Uniform upper bounds on Courant sharp Neumann eigenvalues of chain domains

Thomas Beck; Yaiza Canzani; Jeremy L. Marzuola

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arXiv · 2305.16452

Uniform upper bounds on Courant sharp Neumann eigenvalues of chain domains

Thomas Beck·Yaiza Canzani·Jeremy L. Marzuola

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Abstract

We obtain upper bounds on the number of nodal domains of Laplace eigenfunctions on chain domains with Neumann boundary conditions. The chain domains consist of a family of planar domains, with piecewise smooth boundary, that are joined by thin necks. Our work does not assume a lower bound on the width of the necks in the chain domain. As a consequence, we prove an upper bound on the number of Courant sharp eigenfunctions that is independent of the widths of the necks.

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Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola. 2023-05-25. Uniform upper bounds on Courant sharp Neumann eigenvalues of chain domains. https://arxiv.org/abs/2305.16452

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