10 citations · 17 across the 13 of their papers we have counts for
13 papers
From weighted Carlson-Levin inequalities to weighted Gagliardo-Nirenberg inequalities
Francesco Pagliarin, Nikita Simonov
We study weighted Carlson-Levin inequalities on cones, computing the optimal constant and classifying optimizers via an Entropy method. The limiting case of a logarithmic Carlson-L…
Logarithmic Sobolev inequalities: a review on stability and instability results; logarithmic uncertainty principle
Giovanni Brigati, Jean Dolbeault, Nikita Simonov
In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions o…
Refined asymptotics for the Cauchy problem for the fast -Laplace evolution equation
Matteo Bonforte, Iwona Chlebicka, Nikita Simonov
Our focus is on the fast diffusion equation driven by the -Laplacian operator, that is with , posed in the whole space , . The…
Stability for the logarithmic Sobolev inequality
Giovanni Brigati, Jean Dolbeault, Nikita Simonov
This paper is devoted to stability results for the Gaussian logarithmic Sobolev inequality, with explicit stability constants.
On Gaussian interpolation inequalities
Giovanni Brigati, Jean Dolbeault, Nikita Simonov
This paper is devoted to Gaussian interpolation inequalities with endpoint cases corresponding to the Gaussian Poincaré and the logarithmic Sobolev inequalities, seen as limits in…
Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results
Giovanni Brigati, Jean Dolbeault, Nikita Simonov
We consider Gagliardo-Nirenberg inequalities on the sphere which interpolate between the Poincaré inequality and the Sobolev inequality, and include the logarithmic Sobolev inequal…
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-Sobolev inequalities: flows, regularity and the entropy method
Matteo Bonforte, Jean Dolbeault, Bruno Nazaret +1
The purpose of this work is to establish a quantitative and constructive stability result for a class of subcritical Gagliardo-Nirenberg-Sobolev inequalities which interpolates bet…
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 …