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arXiv · 2411.11168

Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups

Rupert L. Frank·Bernard Helffer·Ari Laptev
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Abstract

We show that the $j$-th Dirichlet eigenvalue of the sub-Laplacian on an open set of a Carnot group is greater than the $(j+1)$-st Neumann eigenvalue. This extends earlier results in the Euclidean and Heisenberg case and has a remarkably simple proof.

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Rupert L. Frank, Bernard Helffer, Ari Laptev. 2024-11-17. Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups. https://arxiv.org/abs/2411.11168

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