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

Yu-Zhao Wang, Yan-Mei Wang

We prove the concavity of $p$-Rényi entropy power for positive solutions to the doubly nonlinear diffusion equations on ${\mathbb{R}}^n$ or compact Riemannian manifolds with nonnegat…