17 citations · 21 across the 5 of their papers we have counts for
8 papers
Weighted Korn and Poincaré-Korn inequalities in the Euclidean space and associated operators
Kleber Carrapatoso, Jean Dolbeault, Frédéric Hérau +2
We prove functional inequalities on vector fields on the Euclidean space when it is equipped with a bounded measure that satisfies a Poincaré inequality, and study associated self-…
Purely magnetic tunneling effect in two dimensions
Virginie Bonnaillie-Noël, Frédéric Hérau, Nicolas Raymond
The semiclassical magnetic Neumann Schrödinger operator on a smooth, bounded, and simply connected domain of the Euclidean plane is considered. When has a symmetry axis, th…
Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker-Planck equations
Guillaume Dujardin, Frédéric Hérau, Pauline Lafitte
In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these discretizations o…
Introduction to hypocoercive methods and applications for simple linear inhomogeneous kinetic models
Frédéric Hérau
In this lectures given at the Morning side center of Mathematics in October 2016, we present in a very simple framework Hilbertian hypocoercive methods in the case of 1d kinetic in…
Short time diffusion properties of inhomogeneous kinetic equations with fractional collision kernel
Frédéric Hérau, Daniela Tonon, Isabelle Tristani
We prove regularization properties in short time for inhomogeneous kinetic equations whose collision kernel behaves like a fractional power of the Laplacian in velocity. We treat a…
Holomorphic extension of the de Gennes function
Virginie Bonnaillie-Noël, Frédéric Hérau, Nicolas Raymond
This note is devoted to prove that the de Gennes function has a holomorphic extension on a strip containing the real axis.
Semiclassical tunneling and magnetic flux effects on the circle
Virginie Bonnaillie-Noël, Frédéric Hérau, Nicolas Raymond
This paper is devoted to semiclassical tunneling estimates induced on the circle by a double well electric potential in the case when a magnetic field is added. When the two electr…
On global existence and trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with exterior confining potential
Frédéric Hérau, Laurent Thomann
We prove a global existence result with initial data of low regularity, and prove the trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with small non linear ter…