Hypoelliptic equations - Open Access .click

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, 2023
Revised ...
Banica, Valeria, Burq, Nicolas
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Regularity for rough hypoelliptic equations

, 2022
We present a general approach to obtain a weak Harnack inequality for rough hypoellipitic equations, e.g. kinetic equations. The proof is constructive and does not study the commutator structure but rather compares the rough solution with a smooth problem for which the estimates are assumed.
Dietert, Helge, Hirsch, Jonas
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Gevrey Hypoellipticity for a Class of Kinetic Equations [PDF]

Communications in Partial Differential 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
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Enhanced dissipation and Taylor dispersion in higher‐dimensional parallel shear flows

Journal of the London Mathematical Society, Volume 108, Issue 4, Page 1358-1392, October 2023., 2023
Abstract We consider the evolution of a passive scalar advected by a parallel shear flow in an infinite cylinder with bounded cross section, in arbitrary space dimension. The essential parameters of the problem are the molecular diffusivity ν$\nu$, which is assumed to be small, and the wave number k$k$ in the streamwise direction, which can take ...
Michele Coti Zelati, Thierry Gallay
wiley +1 more source

Time regularity for generalized Mehler semigroups

Mathematische Nachrichten, Volume 295, Issue 11, Page 2223-2245, November 2022., 2022
Abstract We study continuity and Hölder continuity of t↦Ptf$t\mapsto P_tf$, where Pt$P_t$ is a generalized Mehler semigroup in Cb(X)$C_b(X)$, the space of the continuous and bounded functions from a Banach space X to R$\mathbb {R}$, and f∈Cb(X)$f\in C_b(X)$.
Alessandra Lunardi
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Manifold Markov chain Monte Carlo methods for Bayesian inference in diffusion models

Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 84, Issue 4, Page 1229-1256, September 2022., 2022
Abstract Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology—borrowing ideas from statistical physics and computational chemistry—for ...
Matthew M. Graham +2 more
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Logarithmic Decay for Linear Damped Hypoelliptic Wave and Schrödinger Equations [PDF]

SIAM Journal on Control and Optimization, 2021
We consider damped wave (resp. Schr{ }dinger and plate) equations driven by a hypoelliptic "sum of squares" operator L on a compact manifold and a damping function b(x). We assume the Chow-Rashevski-H{ }rmander condition at rank k (at most k Lie brackets needed to span the tangent space) together with analyticity of M and the coefficients of L.
Laurent, Camille, Léautaud, Matthieu
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Analytic hypoellipticity of Keldysh operators

Proceedings of the London Mathematical Society, Volume 123, Issue 5, Page 498-516, November 2021., 2021
Abstract We consider Keldysh‐type operators, P=x1Dx12+a(x)Dx1+Q(x,Dx′), x=(x1,x′) with analytic coefficients, and with Q(x,Dx′) second order, principally real and elliptic in Dx′ for x near zero. We show that if Pu=f, u∈C∞, and f is analytic in a neighbourhood of 0, then u is analytic in a neighbourhood of 0.
Jeffrey Galkowski, Maciej Zworski
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Almost Periodic Functions and Their Applications: A Survey of Results and Perspectives

Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021
The main aim of this survey article is to present several known results about vector‐valued almost periodic functions and their applications. We separately consider almost periodic functions depending on one real variable and almost periodic functions depending on two or more real variables.
Wei-Shih Du +3 more
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The Heat Equation with Singular Potentials. II: Hypoelliptic Case

Acta Applicandae Mathematicae, 2022
AbstractIn this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded Lie groups. The current work continues and extends the work (Altybay et al. in Appl. Math. Comput.
Marianna Chatzakou +2 more
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