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

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.

Final version to appear in the Journal of Spectral Theory. 15 pages, 2 figures