Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups
Analysis of PDEs
2024-11-19 v1 Spectral Theory
Abstract
We show that the -th Dirichlet eigenvalue of the sub-Laplacian on an open set of a Carnot group is greater than the -st Neumann eigenvalue. This extends earlier results in the Euclidean and Heisenberg case and has a remarkably simple proof.
Cite
@article{arxiv.2411.11168,
title = {Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups},
author = {Rupert L. Frank and Bernard Helffer and Ari Laptev},
journal= {arXiv preprint arXiv:2411.11168},
year = {2024}
}
Comments
10 pages; dedicated to Nikolai Nadirashvili, on the occasion of his 70th birthday