Remarks on hypoelliptic equations
Annales Henri Lebesgue, 2023 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 -hypoellipticity.
V. Banica, N. Burq
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Some Properties of Solutions to Weakly Hypoelliptic Equations [PDF]
International Journal of Differential Equations, 2013 A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size.
Christian Bär
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Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports [PDF]
Comptes Rendus. Mathématique, 2020 We study the null-controllability of some hypoelliptic quadratic parabolic equations posed on the whole Euclidean space with moving control supports, and provide necessary or sufficient geometric conditions on the moving control supports to ensure null ...
Beauchard, Karine +2 more
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Logarithmic Decay for Linear Damped Hypoelliptic Wave and Schrödinger Equations [PDF]
SIAM Journal on Control and Optimization, 2021 \bfA \bfb \bfs \bft \bfr \bfa \bfc \bft . We consider linear damped wave (resp., Schr\"odinger and plate) equations driven by a hypoelliptic ``sum of squares"" operator L on a compact manifold \scrM and a damping function b(x).
C. Laurent, Matthieu Léautaud
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Hypoelliptic convolution equations in the space $\mathscr{H}'{M_p}$
Publicationes Mathematicae Debrecen, 2022 The authors treat the space \({\mathcal H}\{M_ p\}\) of smooth functions \(\phi\) (x) on R such that for every \(p\in {\mathbb{N}}\) \(\gamma_ p(\phi):=\sup \{| \phi^{(j)}(x)| \cdot \exp (M_ p(x));x\in R,0\leq j\leq n\}
S. Pilipovic, A. Takaci
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Hypoelliptic second order differential equations
Acta Mathematica, 1967 L. Hörmander
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The method of stochastic characteristics for linear second-order hypoelliptic equations [PDF]
Probability Surveys, 2021 We study hypoelliptic stochastic differential equations (SDEs) and their connection to degenerate-elliptic boundary value problems on bounded or unbounded domains.
Juraj Foldes, David P. Herzog
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A probabilistic point of view for the Kolmogorov hypoelliptic equations [PDF]
E S A I M: Probability & Statistics, 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 ...
Pierre Etor'e, Jos'e R. Le'on, C. Prieur
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MULTI-TERM TIME-FRACTIONAL DERIVATIVE HEAT EQUATION FOR ONE-DIMENSIONAL DUNKL OPERATOR
Вестник КазНУ. Серия математика, механика, информатика, 2022 In this paper, we investigate the well-posedness for Cauchy problem for multi-term time-fractional heat equation associated with Dunkl operator. The equation under consideration includes a linear combination of Caputo derivatives in time with decreasing ...
D. Serikbaev
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Exponential Mixing and Limit Theorems of Quasi-periodically Forced 2D Stochastic Navier–Stokes Equations in the Hypoelliptic Setting [PDF]
Communications in Mathematical Physics, 2022 We consider the incompressible 2D Navier–Stokes equations on the torus driven by a deterministic time quasi-periodic force and a noise that is white in time and degenerate in Fourier space.
Rongchang Liu, K. Lu
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