Local Spectral Optimisation for Robin Problems with Negative Boundary Parameter on Quadrilaterals
Analysis of PDEs
2023-09-14 v1 Spectral Theory
Abstract
We investigate the Robin eigenvalue problem for the Laplacian with negative boundary parameter on quadrilateral domains of fixed area. In this paper, we prove that the square is a local maximiser of the first eigenvalue with respect to the Hausdorff metric. We also provide asymptotic results relating to the optimality of the square for extreme values of the Robin parameter.
Cite
@article{arxiv.2309.06446,
title = {Local Spectral Optimisation for Robin Problems with Negative Boundary Parameter on Quadrilaterals},
author = {Julie Clutterbuck and James Larsen-Scott},
journal= {arXiv preprint arXiv:2309.06446},
year = {2023}
}
Comments
32 pages, 2 figures