Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896679 | Journal of Functional Analysis | 2018 | 28 Pages |
Abstract
We consider a Riemannian cylinder Ω endowed with a closed potential 1-form A and study the magnetic Laplacian ÎA with magnetic Neumann boundary conditions associated with those data. We establish a sharp lower bound for the first eigenvalue and show that the equality characterizes the situation where the metric is a product. We then look at the case of a planar domain bounded by two closed curves and obtain an explicit lower bound in terms of the geometry of the domain. We finally discuss sharpness of this last estimate.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Bruno Colbois, Alessandro Savo,