Estimates for the Lowest Eigenvalue of Magnetic Laplacians

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...

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Bibliographic Details
Published in:arXiv.org 2015-01
Main Authors: Ekholm, Tomas, Kovarik, Hynek, Portmann, Fabian
Format: Article
Language:English
Subjects:
Dirichlet problem
Eigenvalues
Lower bounds
Upper bounds
Online Access:Get full text
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Summary: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.
ISSN:2331-8422