Related papers: Entropy-type inequalities for generalized Gamma de…
We study partially segregated elliptic systems through the use of penalized energy functionals. These systems arise from the minimization of Gross-Pitaevskii-type energies that capture the behavior of multi-component ultracold gas mixtures…
On the basis of physical considerations we propose a one-dimensional discrete lattice model for the density relaxation of granular materials under tapping. Solving the difference equation numerically, we find a logarithmic time-dependence…
This paper deals with the study of some particular kinetic models, where the randomness acts only on the velocity variable level. Usually, the Markovian generator cannot satisfy any Poincar\'e's inequality. Hence, no Gronwall's lemma can…
We investigate the interactions of functional rearrangements with Prekopa-Leindler type inequalities. It is shown that that a general class of integral inequalities tighten on rearrangement to "isoperimetric" sets with respect to a relevant…
The paper deals with the homogenization of a linear Boltzmann equation by the means of the sigma-convergence method. Under a general deterministic assumption on the coefficients of the equation, we prove that the density of the particles…
We prove a Poincar\'e-Sobolev type inequality on compact Riemannian manifolds where the deviation of a function from a biased average, defined using a density, is controlled by the unweighted Lebesgue norm of its gradient. Unlike classical…
In this paper we establish some explicit and sharp estimates of the spectral gap and the log-Sobolev constant for mean field particles system, uniform in the number of particles, when the confinement potential have many local minimums. Our…
We study the nonlinear Fokker-Planck equation on graphs, which is the gradient flow in the space of probability measures supported on the nodes with respect to the discrete Wasserstein metric. The energy functional driving the gradient flow…
The Gamma-limit of higher-order singular perturbations of the Perona-Malik functional is analyzed. The energies considered combine the critically scaled logarithmic term with a k-th order regularization designed to balance bulk and…
We study the long-time behaviour of a nonlinear Fokker-Planck equation, which models the evolution of rigid polymers in a given flow, after a closure approximation. The aim of this work is twofold: first, we propose a microscopic derivation…
Combining the results of [14] and [10], the trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation. Under some conditions (that allow non-convex confining potentials) the…
We present four types of infinitely many exactly solvable Fokker-Planck equations, which are related to the newly discovered exceptional orthogonal polynomials. They represent the deformed versions of the Rayleigh process and the Jacobi…
We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…
We examine the influence of quenched disorder on the flocking transition of dense polar active matter. We consider incompressible systems of active particles with aligning interactions under the effect of either quenched random forces or…
The present study deals with the inhomogeneous plane symmetric models in scalar - tensor theory of gravitation. We used symmetry group analysis method to solve the field equations analytically. A new class of similarity solutions have been…
The purpose of this short note is to demonstrate uniform logarithmic Sobolev inequalities for the mean field gradient particle systems associated to an energy functional that is convex in the flat sense. A defective log-Sobolev inequality…
In recent years, several fractional generalizations of the usual Kramers-Fokker-Planck equation have been presented. Using an idea of Fogedby [H.C. Fogedby, Phys. Rev. E {\bf 50}, 041103 (1994), we show how these equations are related to…
For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose…
We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex…
This paper investigates the local regularity of solutions to stationary Fokker-Planck equations on an open set $U \subset \mathbb{R}^d$ with $d \geq 2$. A central objective is to relax the classical assumptions on the coefficients by…