A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region
Analysis of PDEs
2025-05-29 v3 Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2409.03908,
title = {A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region},
author = {Lawford Hatcher},
journal= {arXiv preprint arXiv:2409.03908},
year = {2025}
}
Comments
Final version to appear in the Journal of Spectral Theory. 15 pages, 2 figures