Results 11 to 20 of about 4,782 (151)
Analytic hypoellipticity of Keldysh operators [PDF]
Proceedings of the London Mathematical Society, Volume 123, Issue 5, Page 498-516, November 2021., 2020 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
J. Galkowski, M. Zworski
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Local Hypoellipticity by Lyapunov Function
Abstract and Applied Analysis, 2016 We treat the local hypoellipticity, in the first degree, for a class of abstract differential operators complexes; the ones are given by the following differential operators: Lj=∂/∂tj+(∂ϕ/∂tj)(t,A)A, j=1,2,…,n, where A:D(A)⊂H→H is a self-adjoint linear ...
E. R. Aragão-Costa
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Hypoellipticity: Geometrization and Speculation [PDF]
, 1998 To any finite collection of smooth real vector fields $X_j$ in $\reals^n$ we associate a metric in the phase space $T^*\reals^n$. The relation between the asymptotic behavior of this metric and hypoellipticity of $\sum X_j^2$, in the smooth, real ...
Christ, Michael
core +6 more sources
On the regularity of the solutions and of analytic vectors for “sums of squares”
Bruno Pini Mathematical Analysis Seminar, 2023 We present a brief survey on some recent results concerning the local and global regularity of the solutions for some classes/models of sums of squares of vector fields with real-valued real analytic coefficients of H"ormander type.
Gregorio Chinni
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Hypoellipticity and the Mori–Zwanzig formulation of stochastic differential equations [PDF]
Journal of Mathematics and Physics, 2020 We develop a thorough mathematical analysis of the effective Mori-Zwanzig equation governing the dynamics of noise-averaged observables in stochastic differential equations driven by multiplicative Gaussian white noise.
Yuanran Zhu, D. Venturi
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Hypocoercivity and global hypoellipticity for the kinetic Fokker-Planck equation in $ H^k $ spaces [PDF]
Kinetic and Related Models, 2020 The purpose of this paper is to extend the hypocoercivity results for the kinetic Fokker-Planck equation in $H^1$ space in Villani's memoir \cite{Villani} to higher order Sobolev spaces.
Chao Zhang
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Global hypoellipticity and global solvability for vector fields on compact Lie groups [PDF]
Journal of Functional Analysis, 2019 We present necessary and sufficient conditions to have global hypoellipticity and global solvability for a class of vector fields defined on a product of compact Lie groups.
A. Kirilov +2 more
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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
Global analytic hypoellipticity for a class of evolution operators on $\mathbb{T}^1\times\mathbb{S}^3$ [PDF]
, 2020 In this paper, we present necessary and sufficient conditions to have global analytic hypoellipticity for a class of first-order operators defined on $\mathbb{T}^1 \times \mathbb{S}^3$.
A. Kirilov +2 more
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GLOBAL HYPOELLIPTICITY OF SUMS OF SQUARES ON COMPACT MANIFOLDS [PDF]
Journal of the Institute of Mathematics of Jussieu, 2020 We present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on $T \times G$ , where T is a compact Riemannian manifold and G is a compact Lie group.
Gabriel Ara'ujo +2 more
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