Asymptotic eigenvalue estimates for a Robin problem with a large parameter
Mathematical Physics
2019-12-10 v2 math.MP
Spectral Theory
Abstract
Robin problem for the Laplacian in a bounded planar domain with a smooth boundary and a large parameter in the boundary condition is considered. We prove a two-sided three-term asymptotic estimate for the negative eigenvalues. Furthermore, improving the upper bound we get a two term asymptotics in terms of the coupling constant and the maximum of the boundary curvature.
Cite
@article{arxiv.1312.7293,
title = {Asymptotic eigenvalue estimates for a Robin problem with a large parameter},
author = {Pavel Exner and Alexander Minakov and Leonid Parnovski},
journal= {arXiv preprint arXiv:1312.7293},
year = {2019}
}
Comments
This is an extended version of arXiv: 1312.7293~[math-ph], with more coauthors and the upper bound substantially improved; to appear in Portugalia Math