Inequalities between Dirichlet and Neumann Eigenvalues on the Heisenberg Group
File(s)
Accepted version
Author(s)
Frank, RL
Laptev, A
Type
Journal Article
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 kth Dirichlet eigenvalue. As a byproduct, we obtain similar inequalities for the Euclidean Laplacian with a homogeneous magnetic field.
Date Issued
2010-01-05
Date Acceptance
2009-12-02
Citation
International Mathematics Research Notices, 2010, 15, pp.2889-2902
ISSN
1687-0247
Publisher
Oxford University Press (OUP)
Start Page
2889
End Page
2902
Journal / Book Title
International Mathematics Research Notices
Volume
15
Copyright Statement
© 2010 Oxford University Press. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version is available online at: http://dx.doi.org/10.1093/imrn/rnp230
Subjects
Science & Technology
Physical Sciences
Mathematics
MATHEMATICS
DOMAINS
General Mathematics
0101 Pure Mathematics
Publication Status
Published