Results 61 to 70 of about 1,209,225 (153)
The Metivier inequality and ultradifferentiable hypoellipticity
Mathematische Nachrichten, Volume 297, Issue 7, Page 2517-2531, July 2024.Abstract In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of L2$L^2$‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when
Paulo D. Cordaro, Stefan Fürdös
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Hypoelliptic Degenerate Evolution Equations of the Second Order
Publications of the Research Institute for Mathematical Sciences, 1975 For degenerate parabolic differential operators, the study of hypoellipticity has been made by many authors (see [1]~[9]). But for degenerate ]?-parabolie differential operators, its study has not been made so detailed (see F. Treves [10]). So we shall give a sufficient condition for the operator given by (0.1) to be hypoelliptic by constructing very ...
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Bulletin of the London Mathematical Society, Volume 56, Issue 3, Page 981-1003, March 2024.Abstract We study the linear relaxation Boltzmann equation on the torus with a spatially varying jump rate which can be zero on large sections of the domain. In Bernard and Salvarani (Arch. Ration. Mech. Anal. 208 (2013), no. 3, 977–984), Bernard and Salvarani showed that this equation converges exponentially fast to equilibrium if and only if the jump
Josephine Evans, Iván Moyano
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We establish the boundedness of weak subsolutions for a class of degenerate Kolmogorov equations of the hypoelliptic type, compatible with a homogeneous Lie group structure, within bounded product domains using the De Giorgi iteration.
Hou, Mingyi, Hou, Mingyi,
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Hypoelliptic convolution equations in 𝐾’_{𝑝}, 𝑝>1
, 1976 We consider convolution equations in the space K p ′ , p > 1 {K’_p},p > 1 , of distributions which “grow” no faster than ...
G. Sampson, Z. Zieleźny
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Approximate null-controllability with uniform cost for the hypoelliptic Ornstein-Uhlenbeck equations
, 2023 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
Jérémy Martin +3 more
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The Cheeger problem in abstract measure spaces
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract We consider nonnegative σ$\sigma$‐finite measure spaces coupled with a proper functional P$P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space perimeter ...
Valentina Franceschi +3 more
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, 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 +2 more
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On a class of partially hypoelliptic microdifferential equations
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1987 Let M be a real analytic manifold with a complexification X. We consider the microdifferential equation defined in a neighborhood of \(\rho_ 0\in \dot T^*_ MX\) whose principal symbol is written in the form (1) \(p=p_ 1+\sqrt{-1}q_ 1^{2m}p_ 2\) in a neighborhood of \(\rho_ 0\in \dot T^*_ MX\).
Tose, Nobuyuki, Uchida, Moto-o
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Hypoelliptic Multiscale Langevin Diffusions: Large Deviations, Invariant Measures and Small Mass Asymptotics [PDF]
, 2017 We consider a general class of hypoelliptic Langevin diffusions and study two related questions. The first question is large deviations for hypoelliptic multiscale diffusions as the noise and the scale separation parameter go to zero. The second question
Hu, Wenqing +3 more
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