Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group

Details Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group

2009-06-08

arxiv.org/abs/0906.1402v1

Int. Math. Res. Not. 15 (2010), 2889 - 2902

Mathematics

Spectral Theory

10 pages

Scientific paper

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.

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