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

Figalli A.; Maggi F.; Pratelli A.

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

机译：各向异性Sobolev和对数Sobolev不等式在有界变化函数上的尖锐稳定性定理

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摘要

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.

机译：将重排技术与Gromov证明1-Sobolev不等式的证明（通过最佳质量传输）相结合，我们证明了BV（Rn）上各向异性Sobolev不等式的清晰定量形式。作为该结果的推论，我们还得出了各向异性1-log-Sobolev不等式的精确稳定性估计。

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《Advances in Mathematics》 |2013年第null期|共22页
作者
Figalli A.; Maggi F.; Pratelli A.;
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正文语种 eng
中图分类数学;
关键词
Mass transportation; Rearrangement; Sobolev inequalities; Stability;

机译：大众运输;重排;Sobolev不等式;稳定性;

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1. Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation [J] . Figalli A., Maggi F., Pratelli A. Advances in Mathematics . 2013,第Null期

机译：各向异性Sobolev和对数Sobolev不等式在有界变化函数上的尖锐稳定性定理
2. The sharp quantitative Sobolev inequality for functions of bounded variation [J] . Fusco N, Maggi F, Pratelli A Journal of Functional Analysis . 2007,第1期

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3. Sharp Grüss-type Inequalities for Functions whose Derivatives are of Bounded Variation [J] . Sever S. Dragomir Journal of inequalities in pure and applied mathematics . 2007,第4期

机译：导数有界变化的函数的SharpGrüss型不等式
4. Entropy, compound Poisson approximation, log-Sobolev inequalities and measure concentration [C] . Kontoyiannis L., Madiman M. Information Theory Workshop, 2004. IEEE . 2004

机译：熵，复合泊松近似，对数Sobolev不等式和测量浓度
5. On merit functions, error bounds, minimizing and stationary sequences for nonsmooth variational inequality problems [D] . Tan, Lulin 2006

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6. The Trace Theorem the Luzin N- and Morse–Sard Properties for the Sharp Case of Sobolev–Lorentz Mappings [O] . Mikhail V. Korobkov, Jan Kristensen -1

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7. The sharp quantitative Sobolev inequality for functions of bounded variation [O] . N. Fusco, F. Maggi, A. Pratelli 2012

机译：有界变化函数的尖锐的定量Sobolev不等式

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

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