Hypoelliptic estimates for some linear diffusive kinetic equations
نویسندگان
چکیده
منابع مشابه
Sharp Hypoelliptic Estimates for Some Kinetic Equations
We provide a simple overview of some hypoellipticity results with sharp indices for a class of kinetic equations and we outline a general strategy based on some geometrical properties.
متن کاملHypoelliptic Regularity in Kinetic Equations
We establish new regularity estimates, in terms of Sobolev spaces, of the solution f to a kinetic equation. The right-hand side can contain partial derivatives in time, space and velocity, as in classical averaging, and f is assumed to have a certain amount of regularity in velocity. The result is that f is also regular in time and space, and this is related to a commutator identity introduced ...
متن کاملUniform Schauder Estimates for Regularized Hypoelliptic Equations
In this paper we are concerned with a family of elliptic operators represented as sum of square vector fields: L = ∑m i=1X 2 i + ∆ in Rn, where ∆ is the Laplace operator, m < n, and the limit operator L = ∑m i=1X 2 i is hypoelliptic. Here we establish Schauder’s estimates, uniform with respect to the parameter , of solution of the approximated equation L u = f , using a modification of the lift...
متن کاملAnalysis of Asymptotic Preserving DG-IMEX Schemes for Linear Kinetic Transport Equations in a Diffusive Scaling
In this paper, some theoretical aspects will be addressed for the asymptotic preserving DG-IMEX schemes recently proposed in [10] for kinetic transport equations under a diffusive scaling. We will focus on the methods that are based on discontinuous Galerkin (DG) spatial discretizations with the P k polynomial space and a first order IMEX temporal discretization, and apply them to two linear mo...
متن کاملHypoelliptic estimates in radiative transfer
We derive the hypoelliptic estimates for a kinetic equation of the form ∂tf + k · ∇xf = (−∆d)h, for (t, x, k) ∈ R× R × S, where d ≥ 1, β > 0, Sd is the unit sphere in Rd+1 and ∆d is the Laplace-Beltrami operator on Sd. Such equations arise in the modeling of high frequency waves in random media with long-range correlations. Assuming some (fractional) Sobolev regularity in the momentum variable ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journées Équations aux dérivées partielles
سال: 2010
ISSN: 0752-0360
DOI: 10.5802/jedp.66