Maximization of the second non-trivial Neumann eigenvalue
Analysis of PDEs
2018-01-24 v1
Abstract
In this paper we prove that the second (non-trivial) Neumann eigenvalue of the Laplace operator on smooth domains of R N with prescribed measure m attains its maximum on the union of two disjoint balls of measure m 2. As a consequence, the P{\'o}lya conjecture for the Neumann eigenvalues holds for the second eigenvalue and for arbitrary domains. We moreover prove that a relaxed form of the same inequality holds in the context of non-smooth domains and densities.
Cite
@article{arxiv.1801.07435,
title = {Maximization of the second non-trivial Neumann eigenvalue},
author = {Dorin Bucur and Antoine Henrot},
journal= {arXiv preprint arXiv:1801.07435},
year = {2018}
}