Calculus of Variations and Geometric Measure Theory

A. Figalli - F. Maggi - A. Pratelli

Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation

created by maggi on 05 Sep 2011
modified by pratelli on 16 Feb 2015


Published Paper

Inserted: 5 sep 2011
Last Updated: 16 feb 2015

Journal: Adv. Math.
Year: 2012


Combining rearrangement techniques with GromovÂ’s proof (via optimal mass transportation) of the 1-Sobolev inequality, we prove a sharp quantitative version of the anisotropic Sobolev inequality on BV (Rn). As a corollary of this result, we also deduce a sharp stability estimate for the anisotropic 1-log-Sobolev inequality.