The concavity of \(p\)-entropy power and applications in functional inequalities

DOI10.1016/j.na.2018.07.018zbMath1404.35273arXiv1902.00904OpenAlexW2889426037MaRDI QIDQ1633674

Yu-Zhao Wang, Xin-xin Zhang

Publication date: 20 December 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.00904

zbMATH Keywords

concavitylogarithmic Sobolev inequalityNash inequalityentropy power inequality\(p\)-heat equation

Mathematics Subject Classification ID

Heat and other parabolic equation methods for PDEs on manifolds (58J35) Quasilinear parabolic equations with (p)-Laplacian (35K92)

Related Items (5)

Generalized displacement convexity for nonlinear mobility continuity equation and entropy power concavity on Wasserstein space over Riemannian manifolds ⋮ Rigidity results for the p‐Laplace type equations on compact Riemannian manifolds ⋮ The log entropy formula and entropy power for \(p\)-heat equation on Riemannian manifolds ⋮ The concavity of \(p\)-Rényi entropy power for doubly nonlinear diffusion equations and \(L^p\)-Gagliardo-Nirenberg-Sobolev inequalities ⋮ The concavity of Rényi entropy power for the parabolic \(p\)-Laplace equations and applications

Cites Work

• A Mathematical Theory of Communication
• Sharp Gagliardo-Nirenberg inequalities via \(p\)-Laplacian type equations
• The general optimal \(L^{p}\)-Euclidean logarithmic Sobolev inequality by Hamilton--Jacobi equations.
• The optimal Euclidean \(L^{p}\)-Sobolev logarithmic inequality.
• Gradient estimates and entropy formulae for weighted \(p\)-heat equations on smooth metric measure spaces
• An information-theoretic proof of Nash's inequality
• Differential Harnack estimates and entropy formulae for weighted \(p\)-heat equations
• The Concavity of Rényi Entropy Power
• Local gradient estimates of $p$-harmonic functions, $1/H$-flow, and an entropy formula
• A new entropy power inequality
• A short proof of the "concavity of entropy power"
• Analysis and Geometry of Markov Diffusion Operators

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