Calculus of Variations and Geometric Measure Theory

A. Figalli - Y. R. Y. Zhang

Sharp gradient stability for the Sobolev inequality

created by figalli on 05 Aug 2021
modified on 19 Aug 2024

[BibTeX]

Published Paper

Inserted: 5 aug 2021
Last Updated: 19 aug 2024

Journal: Duke Math. J.
Year: 2022

Abstract:

We prove a sharp quantitative version of the $p$-Sobolev inequality for any $1<p<n$, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for $p \leq 2$, while it depends on $p$ for $p>2$.


Download: