A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region

Autor:	Hatcher, Lawford
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Mathematics - Spectral Theory 35P05 35B38 35J05 35J25 58J50
Druh dokumentu:	Working Paper
Popis:	We prove that on convex domains, first mixed Laplace eigenfunctions have no interior critical points if the Dirichlet region is connected and sufficiently small. We also find two seemingly new estimates on the first mixed eigenvalue to give explicit examples of when the Dirichlet region is sufficiently small. Comment: Added two new theorems related to the optimization of the first mixed eigenvalue. Also updated the exposition and added new examples. 9 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.03908 Zobrazit plný text záznamu View this record from Arxiv