Sharp Stability Theorems for the Anisotropic Sobolev and Log-sobolev Inequalities on Functions of Bounded Variation

نویسنده

A. FIGALLI

چکیده

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 (R). As a corollary of this result, we also deduce a sharp stability estimate for the anisotropic 1-log-Sobolev inequality.

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