Calculus of Variations and Geometric Measure Theory

A. Figalli - R. Neumayer

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

created by figalli on 26 Sep 2016


Accepted Paper

Inserted: 26 sep 2016
Last Updated: 26 sep 2016

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


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.