Robin spectrum: two disks maximize the third eigenvalue
Spectral Theory
2019-08-01 v1 Analysis of PDEs
Abstract
The third eigenvalue of the Robin Laplacian on a simply-connected planar domain of given area is bounded above by the third eigenvalue of a disjoint union of two disks, provided the Robin parameter lies in a certain range and is scaled in each case by the length of the boundary. Equality is achieved when the domain degenerates suitably to the two disks.
Cite
@article{arxiv.1907.13173,
title = {Robin spectrum: two disks maximize the third eigenvalue},
author = {Alexandre Girouard and Richard S. Laugesen},
journal= {arXiv preprint arXiv:1907.13173},
year = {2019}
}
Comments
32 pages, 8 figures