Gradient stability for the Sobolev inequality: the case
Alessio Figalli
ETH Zürich, SwitzerlandRobin Neumayer
Northwestern University, Evanston, USA
![Gradient stability for the Sobolev inequality: the case $p\geq 2$ cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-21-issue-2.png&w=3840&q=90)
Abstract
We show a strong form of the quantitative Sobolev inequality in for , where the deficit of a function controls for an extremal function in the Sobolev inequality.
Cite this article
Alessio Figalli, Robin Neumayer, Gradient stability for the Sobolev inequality: the case . J. Eur. Math. Soc. 21 (2019), no. 2, pp. 319–354
DOI 10.4171/JEMS/837