Elsevier

Advances in Mathematics

Volume 242, 1 August 2013, Pages 80-101
Advances in Mathematics

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

https://doi.org/10.1016/j.aim.2013.04.007Get rights and content
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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(Rn). We also deduce, as a corollary of this result, a sharp stability estimate for the anisotropic 1-log-Sobolev inequality.

Keywords

Sobolev inequalities
Stability
Rearrangement
Mass transportation

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