Rnyi Entropies and Nonlinear Diffusion Equations
Since their introduction in the early sixties (Rnyi in Proc. Fourth Berkeley Symp. Math. Statist. Prob., vol.1, pp.547561, 1961), the Rnyi entropies have been used in many contexts, ranging from information theory to astrophysics, turbulence phenomena and others. In this note, we enlighten the main connections between Rnyi entropies and nonlinear diffusion equations. In particular, it is shown that these relationships allow to prove various functional inequalities in sharp form.
rnyi entropy nonlinear diffusion equations sobolev type inequalities 94a17 60e99