On the lowest eigenvalue of Laplace operators with mixed boundary conditions
Mathematical Physics
2012-12-18 v1 Analysis of PDEs
math.MP
Spectral Theory
Abstract
In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions.
Keywords
Cite
@article{arxiv.1208.3396,
title = {On the lowest eigenvalue of Laplace operators with mixed boundary conditions},
author = {Hynek Kovarik},
journal= {arXiv preprint arXiv:1208.3396},
year = {2012}
}