Ari Laptev

activity

20242026

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2 papers · 1 filter

math.AP2024

Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups

Rupert L. Frank, Bernard Helffer, Ari Laptev

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 i…

math.AP2024

Hardy inequalities for large fermionic systems

Rupert L. Frank, Thomas Hoffmann-Ostenhof, Ari Laptev +1

Given $0 < s < \frac{d}{2}$ with $s \leq 1$ , we are interested in the large $N$ -behavior of the optimal constant $κ_{N}$ in the Hardy inequality $\sum_{n=1}^N (-Δ_n)^s \geq κ_N \sum_{n<m} |X…