# Gradient stability for the Sobolev inequality: the case $p\geq 2$

created by figalli on 26 Sep 2016

[BibTeX]

Accepted Paper

Inserted: 26 sep 2016
Last Updated: 26 sep 2016

Journal: J. Eur. Math. Soc. (JEMS)
Year: 2016

Abstract:

We prove a strong form of the quantitative Sobolev inequality in $\mathbb{R}^n$ for $p\geq 2$, where the deficit of a function $u\in \dot W^{1,p}$ controls $\ \nabla u -\nabla v\ _{L^p}$ for an extremal function $v$ in the Sobolev inequality.