Local Spectral Optimisation for Robin Problems with Negative Boundary Parameter on Quadrilaterals
Year: 2023
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Clutterbuck, Julie, Larsen-Scott, James
Institution: Monash University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4386793428