Results 31 to 40 of about 425 (156)

Hypoellipticity and the Mori–Zwanzig formulation of stochastic differential equations [PDF]

Journal of Mathematical Physics, 2021
We develop a thorough mathematical analysis of the effective Mori–Zwanzig (EMZ) equation governing the dynamics of noise-averaged observables in stochastic differential equations driven by multiplicative Gaussian white noise. Building upon recent work on hypoelliptic operators, we prove that the EMZ memory kernel and fluctuation terms converge ...
Yuanran Zhu, Daniele Venturi
openaire   +5 more sources

Liouville theorems in halfspaces for parabolic hypoelliptic equations [PDF]

, 2006
We prove some one-side Liouville-type theorems in halfspaces for a class of evolution hypoelliptic equations. The operators we deal with are left translation invariant, and homogeneous of degree two, on homogeneous Lie groups on $mathbb{R}^{N+1}$
Lanconelli, Ermanno, Ermanno Lanconelli, KOGOJ, ALESSIA ELISABETTA   +2 more
core   +1 more source

Hypoellipticity for a class of kinetic equations

Kyoto Journal of Mathematics, 2007
The authors consider the following linearized version of Boltzmann equation without angular cutoff: \[ Pu= \partial_t+ x\nabla_y u+ \sigma(-\widetilde\Delta_x)^\lambda u= f, \] where \((x,y)\in \mathbb{R}^{2n}\) and \(\sigma> 0\). Here \((-\widetilde\Delta_x)^\lambda\) is a Fourier multiplier with symbol \(|\eta|^{2\lambda}\) if \(|\eta|\geq 2\), and \(
Xu, Chao-Jiang, Morimoto, Yoshinori
openaire   +4 more sources

Theory of B(X)‐Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators

Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020
The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from generally unbounded infinitesimal generators.
Yoritaka Iwata, Ricardo Weder
wiley   +1 more source

Uniform Schauder estimates for regularized hypoelliptic equations [PDF]

, 2009
In this paper we are concerned with a family of elliptic operators represented as sum of square vector fields and the limit operator is hypoelliptic. Here we establish Schauder's estimates, uniform with respect to the parameter , of solution of ...
MANFREDINI, MARIA
core   +1 more source

On the Dirichlet problem for hypoelliptic evolution equations: Perron–Wiener solution and a cone-type criterion [PDF]

, 2017
We show how to apply harmonic spaces potential theory in the study of the Dirichlet problem for a general class of evolution hypoelliptic partial differential equations of second order.
KOGOJ, ALESSIA ELISABETTA
core   +1 more source

A probabilistic point of view for the exact or approximated computation of the solution to Kolmogorov hypoelliptic equations [PDF]

, 2021
In this work, we propose a method for solving Kolmogorov hypoelliptic equations based on Fourier transform and Feynman-Kac formula. We first explain how the Feynman-Kac formula can be used to compute the fundamental solution to parabolic equations with ...
Prieur, Clémentine, León, Jose,, Etoré, Pierre   +2 more
core  

Globally hypoelliptic and globally solvable first-order evolution equations [PDF]

, 1979
We consider global hypoellipticity and global solvability of abstract first order evolution equations defined either on an interval or in the unit circle, and prove that it is equivalent to certain conditions bearing on the total symbol.
Jorge Hounie
core   +1 more source

Remarks on hypoelliptic equations

Annales Henri Lebesgue
Many results of smooth hypoellipticity are available for scalar equations. Much remains to be done for systems and/or at different levels of regularity and in particular for L 1
Banica, Valeria, Burq, Nicolas
openaire   +2 more sources

The Gevrey hypoellipticity for kinetic equations

, 2011
In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.
Chen, Hua, Li, Weixi, Xu, Chao-Jiang
openaire   +2 more sources