Uniform upper bounds on Courant sharp Neumann eigenvalues of chain domains

Autor:	Beck, Thomas, Canzani, Yaiza, Marzuola, Jeremy L.
Rok vydání:	2023
Předmět:	Mathematics - Spectral Theory Mathematics - Analysis of PDEs 35P99 58J50
Druh dokumentu:	Working Paper
Popis:	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. Comment: 33 pages, 3 figures, comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.16452 Zobrazit plný text záznamu View this record from Arxiv