Optimisation of the lowest Robin eigenvalue in the exterior of a compact set
Spectral Theory
2018-11-26 v2 Mathematical Physics
Analysis of PDEs
math.MP
Optimization and Control
Abstract
We consider the problem of geometric optimisation of the lowest eigenvalue of the Laplacian in the exterior of a compact planar set, subject to attractive Robin boundary conditions. Under either a constraint of fixed perimeter or area, we show that the maximiser within the class of exteriors of convex sets is always the exterior of a disk. We also argue why the results fail without the convexity constraint and in higher dimensions.
Keywords
Cite
@article{arxiv.1608.04896,
title = {Optimisation of the lowest Robin eigenvalue in the exterior of a compact set},
author = {David Krejcirik and Vladimir Lotoreichik},
journal= {arXiv preprint arXiv:1608.04896},
year = {2018}
}
Comments
13 pages; counterexample in Section 5.3 corrected; to appear in Journal of Convex Analysis