Rupert L. Frank

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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…

math.AP2024

On the sharp constants in the regional fractional Sobolev inequalities

Rupert L. Frank, Tianling Jin, Wei Wang

In this paper, we study the sharp constants in fractional Sobolev inequalities associated with the regional fractional Laplacian in domains.