Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group
Spectral Theory
2011-09-05 v1
Abstract
We prove that for any domain in the Heisenberg group the (k+1)'th Neumann eigenvalue of the sub-Laplacian is strictly less than the k'th Dirichlet eigenvalue. As a byproduct we obtain similar inequalities for the Euclidean Laplacian with a homogeneous magnetic field.
Keywords
Cite
@article{arxiv.0906.1402,
title = {Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group},
author = {Rupert L. Frank and Ari Laptev},
journal= {arXiv preprint arXiv:0906.1402},
year = {2011}
}
Comments
10 pages