The first Robin eigenvalue with negative boundary parameter
Spectral Theory
2015-07-31 v2 Mathematical Physics
math.MP
Optimization and Control
Abstract
We give a counterexample to the long standing conjecture that the ball maximises the first eigenvalue of the Robin eigenvalue problem with negative parameter among domains of the same volume. Furthermore, we show that the conjecture holds in two dimensions provided that the boundary parameter is small. This is the first known example within the class of isoperimetric spectral problems for the first eigenvalue of the Laplacian where the ball is not an optimiser.
Cite
@article{arxiv.1403.6666,
title = {The first Robin eigenvalue with negative boundary parameter},
author = {Pedro Freitas and David Krejcirik},
journal= {arXiv preprint arXiv:1403.6666},
year = {2015}
}
Comments
15 pages; extension of the positive result to multiply connected domains