391 citations · 1.8k across the 147 of their papers we have counts for
47 papers · 1 filter
Degenerate Stability of the Caffarelli-Kohn-Nirenberg Inequality along the Felli-Schneider Curve
Rupert L. Frank, Jonas W. Peteranderl
We show that the Caffarelli-Kohn-Nirenberg (CKN) inequality holds with a remainder term that is quartic in the distance to the set of optimizers for the full parameter range of the…
Minimizers for an aggregation model with attractive-repulsive interaction
Rupert L. Frank, Ryan W. Matzke
We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances.…
The sharp Sobolev inequality and its stability: An introduction
Rupert L. Frank
These notes are an extended version of a series of lectures given at the CIME Summer School in Cetraro in June 2022. The goal is to explain questions about optimal functional inequ…
On Sobolev norms involving Hardy operators in a half-space
Rupert L. Frank, Konstantin Merz
We consider Hardy operators on the half-space, that is, ordinary and fractional Schrödinger operators with potentials given by the appropriate power of the distance to the boundary…
Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence
Jean Dolbeault, Maria J. Esteban, Alessio Figalli +2
We prove a sharp quantitative version for the stability of the Sobolev inequality with explicit constants. Moreover, the constants have the correct behavior in the limit of large d…
An improved one-dimensional Hardy inequality
Rupert L. Frank, Ari Laptev, Timo Weidl
We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a consequence of this new inequality we ca…