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 figalli on 13 Aug 2024

[BibTeX]

Published Paper

Inserted: 5 sep 2011
Last Updated: 13 aug 2024

Journal: Adv. Math.
Year: 2013

Abstract:

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


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