A short review on Improvements and stability for some interpolation inequalities
Analysis of PDEs
2024-04-23 v2
Abstract
In this paper, we present recent stability results with explicit and dimensionally sharp constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic Sobolev inequality obtained by the authors in [24]. The stability for the Gaussian logarithmic Sobolev inequality was obtained as a byproduct of the stability for the Sobolev inequality. Here we give a new, direct, alternative proof. We also discuss improved versions of interpolation inequalities based on the carr\'e du champ method.
Keywords
Cite
@article{arxiv.2402.08527,
title = {A short review on Improvements and stability for some interpolation inequalities},
author = {Jean Dolbeault and Maria J. Esteban and Alessio Figalli and Rupert Frank and Michael Loss},
journal= {arXiv preprint arXiv:2402.08527},
year = {2024}
}