Rupert L. Frank

activity

20162026

collaborators

8 papers

math.AP2026

Sharp Sobolev inequalities under first moment constraints

Rupert L. Frank, Tianling Jin, Hua-Yang Wang +1

Let $n \geq 2$ and $1 < p < n$ . We study sharp Sobolev inequalities on the round sphere $S^{n}$ for functions $u \in W^{1, p} (S^{n})$ satisfying $\int_{\mathbb{S}^n}x|u|^{np/…

math.FA2026

Another characterization of $W ˙^{1, p} (R^{d})$

Rupert L. Frank

We improve an earlier characterization of the Sobolev space $W ˙^{1, p} (R^{d})$ , $1 < p < \infty$ , in terms of the oscillations of a function on balls of varying centers and ra…

math.FA2024

Endpoint Schatten class properties of commutators

Rupert L. Frank, Fedor Sukochev, Dmitriy Zanin

We study trace ideal properties of the commutators $[(- Δ)^{\frac{ε}{2}}, M_{f}]$ of a power of the Laplacian with the multiplication operator by a function $f$ on $R^{d}$ . For a c…

math-ph2024

Lieb-Thirring inequality for the 2D Pauli operator

Rupert L. Frank, Hynek Kovařík

By the Aharonov-Casher theorem, the Pauli operator $P$ has no zero eigenvalue when the normalized magnetic flux $α$ satisfies $∣ α ∣ < 1$ , but it does have a zero energy resonance. We…

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.

math-ph2023

Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator

Giao Ky Duong, Rupert L. Frank, Thi Minh Thao Le +2

We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schrödinger operator $- Δ - (d - 2)^{2} / (4∣ x ∣^{2}) - W (x)$ on $L^{2} (R^{d})$ . The b…

math-ph2016

The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory

Rupert L. Frank, Phan Thành Nam, Hanne Van Den Bosch

We prove that in Thomas-Fermi-Dirac-von Weizsäcker theory, a nucleus of charge $Z > 0$ can bind at most $Z + C$ electrons, where $C$ is a universal constant. This result is obtained th…