206 citations · 1.1k across the 65 of their papers we have counts for
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Stability results for logarithmic Sobolev and Gagliardo-Nirenberg inequalities
Jean Dolbeault, Giuseppe Toscani
This paper is devoted to improvements of functional inequalities based on scalings and written in terms of relative entropies. When scales are taken into account and second moments…
A concavity property for the reciprocal of Fisher information and its consequences on Costa's EPI
G. Toscani
We prove that the reciprocal of Fisher information of a log-concave probability density in is concave in with respect to the addition of a Gaussian noise $Z_t…
A strengthened entropy power inequality for log-concave densities
Giuseppe Toscani
We show that Shannon's entropy--power inequality admits a strengthened version in the case in which the densities are log-concave. In such a case, in fact, one can extend the Blach…
Best matching Barenblatt profiles are delayed
Jean Dolbeault, Giuseppe Toscani
The growth of the second moments of the solutions of fast diffusion equations is asymptotically governed by the behavior of self-similar solutions. However, at next order, there is…
On Rosenau-Type Approximations to Fractional Diffusion Equations
Giulia Furioli, Ada Pulvirenti, Elide Terraneo +1
Owing to the Rosenau argument in Physical Review A, 46 (1992), pag. 12-15, originally proposed to obtain a regularized version of the Chapman-Enskog expansion of hydrodynamics, we…
Renyi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations
J. A. Carrillo, G. Toscani
We investigate the large-time asymptotics of nonlinear diffusion equations in dimension , in the exponent interval , when the initial datum …