A counterexample to Payne's nodal line conjecture with few holes
Spectral Theory
2021-07-28 v1 Analysis of PDEs
Abstract
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoffmann-Ostenhof and Nadirashvili proved this to be false by constructing a counterexample in the plane with many holes and raised the question of the minimum number of holes a counterexample can have. In this paper we prove it is at most 6.
Cite
@article{arxiv.2103.02276,
title = {A counterexample to Payne's nodal line conjecture with few holes},
author = {Joel Dahne and Javier Gómez-Serrano and Kimberly Hou},
journal= {arXiv preprint arXiv:2103.02276},
year = {2021}
}
Comments
17 pages, 7 figures, 2 tables