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

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.

16 pages

Cited by in corpus (1)

• The concavity of $p$-Rényi entropy power for doubly nonlinear diffusion equations and $L^p$-Gagliardo-Nirenberg-Sobolev inequalities