Estimates for the Lowest Eigenvalue of Magnetic Laplacians
Spectral Theory
2015-01-23 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a bounded domain in two dimensions. When the magnetic field is constant, we give lower and upper bounds in terms of geometric quantities of the domain. We furthermore prove a lower bound for the first magnetic Neumann eigenvalue in the case of constant field.
Keywords
Cite
@article{arxiv.1501.05554,
title = {Estimates for the Lowest Eigenvalue of Magnetic Laplacians},
author = {Tomas Ekholm and Hynek Kovarik and Fabian Portmann},
journal= {arXiv preprint arXiv:1501.05554},
year = {2015}
}
Comments
19 pages