Sharp gradient stability for the Sobolev inequality

Monday, 9 March, 2020

Published in: 

arXiv:2003.04037

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<2, while it depends on p for p>2.

Author(s): 

Alessio Figalli
Yi Ru-Ya Zhang