Results 11 to 20 of about 3,513,590 (164)
Quantitative spectral gaps for hypoelliptic stochastic differential equations with small noise [PDF]
Probability and Mathematical Physics, 2021 We study the convergence rate to equilibrium for a family of Markov semigroups $\{\mathcal{P}_t^{\epsilon}\}_{\epsilon > 0}$ generated by a class of hypoelliptic stochastic differential equations on $\mathbb{R}^d$, including Galerkin truncations of the ...
J. Bedrossian, Kyle L. Liss
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Approximate Null-Controllability with Uniform Cost for the Hypoelliptic Ornstein-Uhlenbeck Equations [PDF]
SIAM Journal of Control and Optimization, 2022 We prove that the approximate null-controllability with uniform cost of the hypoelliptic Ornstein-Uhlenbeck equations posed on $\mathbb R^n$ is characterized by an integral thickness geometric condition on the control supports. We also provide associated
P. Alphonse, J'er'emy Martin
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Fractional SchrÖdinger Equations with Singular Potentials of Higher Order. II: Hypoelliptic Case [PDF]
Reports on mathematical physics, 2021 In this paper we consider the space-fractional Schrödinger equation with a singular potential for a wide class of fractional hypoelliptic operators. Such analysis can be conveniently realised in the setting of graded Lie groups.
M. Chatzakou +2 more
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Some global Sobolev inequalities related to Kolmogorov-type operators
Bruno Pini Mathematical Analysis Seminar, 2020 In this note we review a recent result in [17] in collaboration with N. Garofalo, where we establish global versions of Hardy-Littlewood-Sobolev inequalities attached to hypoelliptic equations of Kolmogorov type.
Giulio Tralli
doaj +1 more source
Functional inequalities for a class of nonlocal hypoelliptic equations of Hörmander type [PDF]
Nonlinear Analysis, 2019 We consider a class of second-order partial differential operators $\mathscr A$ of Hormander type, which contain as a prototypical example a well-studied operator introduced by Kolmogorov in the '30s.
N. Garofalo, G. Tralli
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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
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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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Quantitative unique continuation for hyperbolic and hypoelliptic equations
Séminaire Laurent Schwartz — EDP et applications, 2020 We review recent results of the authors concerning quantitative unique continuation estimates for operators with coefficients that are analytic in some (or all the) variables.
C. Laurent, Matthieu Léautaud
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