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The concavity of $p$-Rényi entropy power for doubly nonlinear diffusion equations and $L^p$-Gagliardo-Nirenberg-Sobolev inequalities (1911.10525v1)
Published 24 Nov 2019 in math.AP and math.DG
Abstract: We prove the concavity of $p$-R\'enyi entropy power for positive solutions to the doubly nonlinear diffusion equations on $\mathbb{R}n$ or compact Riemannian manifolds with nonnegative Ricci curvature. As applications, we give new proofs of the sharp $Lp$-Sobolev inequality and $Lp$-Gagliardo-Nirenberg inequalities on $\mathbb{R}n$. Moreover, two improvement of $Lp$-Gagliardo-Nirenberg inequalities are derived.