Anisotropic hypoelliptic estimates for Landau-type operators

DOI10.1016/j.matpur.2010.11.003zbMath1221.35107arXiv1003.3265OpenAlexW2027124599MaRDI QIDQ536206

Karel Pravda-Starov, Frederic Hérau

Publication date: 16 May 2011

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.3265

zbMATH Keywords

loss of derivativesLandau equationanisotropic diffusionWick quantizationsub-elliptic estimatesWeyl-Hörmander pseudo-differential operators

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Hypoelliptic equations (35H10) Subelliptic equations (35H20) Fokker-Planck equations (35Q84)

Related Items (14)

An \(L^2\) to \(L^\infty\) framework for the Landau equation ⋮ \(L^{2}\)-regularity of kinetic equations with external potential ⋮ Global hypoelliptic estimates for Landau-type operators with external potential ⋮ Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff ⋮ Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials ⋮ Compactness in kinetic transport equations and hypoellipticity ⋮ Compactness properties and local existence of weak solutions to the Landau equation ⋮ Hypoelliptic Estimates for a Linear Model of the Boltzmann Equation Without Angular Cutoff ⋮ The Landau equation with the specular reflection boundary condition ⋮ Global hypoelliptic estimates for fractional order kinetic equation ⋮ Gelfand-Shilov and Gevrey smoothing effect of the Cauchy problem for Fokker-Planck equation ⋮ Hypocoercivity for linear kinetic equations conserving mass ⋮ Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation ⋮ The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off

Cites Work

• Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff
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• Ultra-analytic effect of Cauchy problem for a class of kinetic equations
• Hypoelliptic differential operators and nilpotent groups
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• The Landau equation in a periodic box
• Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
• Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations
• Hypoellipticity for a class of kinetic equations
• Hypoelliptic second order differential equations
• Subelliptic estimates for quadratic differential operators
• The uncertainty principle and sharp gårding inequalities
• La condition de hörmander-khon pour les operateurs pseudo-differentiels
• Semiclassical Analysis for the Kramers–Fokker–Planck Equation
• Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
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