The Sharp Quantitative Sobolev Inequality for Functions of Bounded Variation
نویسنده
چکیده
The classical Sobolev embedding theorem of the space of functions of bounded variation BV (Rn) into Ln (Rn) is proved in a sharp quantitative form.
منابع مشابه
Sharp Stability Theorems for the Anisotropic Sobolev and Log-sobolev Inequalities on Functions of Bounded Variation
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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