A variational approach to the hot spots conjecture
Spectral Theory
2024-04-03 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We review a recent new approach to the study of critical points of Laplacian eigenfunctions. Its core novelty is a non-standard variational principle for the eigenvalues of the Laplacians with Neumann and Dirichlet boundary conditions on bounded, simply connected planar domains. This principle can be used to provide simple proofs of some previously known results on the hot spots conjecture.
Cite
@article{arxiv.2404.01890,
title = {A variational approach to the hot spots conjecture},
author = {Jonathan Rohleder},
journal= {arXiv preprint arXiv:2404.01890},
year = {2024}
}
Comments
Survey / review paper, written as extended abstract of a lecture given at the Ghent Geometric Analysis Seminar. To appear in Extended Abstracts 2021/2022, Methusalem Lectures, Trends Math. 2024