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.
Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation / A. Figalli; F. Maggi; A. Pratelli. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 242:(2013), pp. 80-101. [10.1016/j.aim.2013.04.007]
Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation
MAGGI, FRANCESCO;
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(Rn). We also deduce, as a corollary of this result, a sharp stability estimate for the anisotropic 1-log-Sobolev inequality.
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