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arXiv · 1902.00904

The concavity of $p$-entropy power and applications in functional inequalities

Yu-Zhao Wang·Xinxin Zhang
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Abstract

In this paper, we prove the concavity of $p$-entropy power of probability densities solving the $p$-heat equation on closed Riemannian manifold with nonnegative Ricci curvature. As applications, we give new proofs of $L^p$-Euclidean Nash inequality and $L^p$-Euclidean Logarithmic Sobolev inequality, moreover, an improvement of $L^p$-Logarithmic Sobolev inequality is derived.

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Yu-Zhao Wang, Xinxin Zhang. 2019-02-03. The concavity of $p$-entropy power and applications in functional inequalities. https://arxiv.org/abs/1902.00904

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