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Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations
Matteo Bonforte, Jean Dolbeault, Bruno Nazaret +1
We provide a scheme of a recent stability result for a family of Gagliardo-Nirenberg-Sobolev (GNS) inequalities, which is equivalent to an improved entropy - entropy production ine…
Functional inequalities and applications to doubly nonlinear diffusion equations
Iwona Chlebicka, Nikita Simonov
We study weighted inequalities of Hardy and Hardy-Poincaré type and find necessary and sufficient conditions on the weights so that the considered inequalities hold. Examples with…
The Cauchy problem for the fast Laplacian evolution equation. Characterization of the global Harnack principle and fine asymptotic behaviour
Matteo Bonforte, Nikita Simonov, Diana Stan
We study fine global properties of nonnegative solutions to the Cauchy Problem for the fast -Laplacian evolution equation on the whole Euclidean space, in the so-cal…
Stability in Gagliardo-Nirenberg inequalities - Supplementary material
Matteo Bonforte, Jean Dolbeault, Bruno Nazaret +1
This document comes as supplementary material of the paper Stability in Gagliardo-Nirenberg inequalities by the same authors. It is intended to state a number of classical or eleme…
Fine properties of solutions to the Cauchy problem for a Fast Diffusion Equation with Caffarelli-Kohn-Nirenberg weights
Matteo Bonforte, Nikita Simonov
We investigate fine global properties of nonnegative, integrable solutions to the Cauchy problem for the Fast Diffusion Equation with weights (WFDE) $u_t=|x|^γ\mathrm{div}\left(|x|…
Quantitative a Priori Estimates for Fast Diffusion Equations with Caffarelli-Kohn-Nirenberg weights. Harnack inequalities and Hölder continuity
Matteo Bonforte, Nikita Simonov
We study a priori estimates for a class of non-negative local weak solution to the weighted fast diffusion equation , with …