Hölder Continuity for a Family of Nonlocal Hypoelliptic Kinetic Equations

DOI10.1137/18M1234953zbMath1430.35065arXiv1812.09006OpenAlexW2994487311MaRDI QIDQ5203763

Logan F. Stokols

Publication date: 9 December 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.09006

zbMATH Keywords

Fokker-Planck equationHölder regularityfractional LaplacianhypoellipticDe Giorgi method

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Hypoelliptic equations (35H10) Integro-differential operators (47G20) Fokker-Planck equations (35Q84)

Related Items (7)

Regularity for the Boltzmann equation conditional to macroscopic bounds ⋮ Quantitative De Giorgi methods in kinetic theory for non-local operators ⋮ Kinetic maximal \(L_\mu^p(L^p)\)-regularity for the fractional Kolmogorov equation with variable density ⋮ Hölder regularity up to the boundary for critical SQG on bounded domains ⋮ Pencil-beam approximation of fractional Fokker-Planck ⋮ Velocity Averaging and Hölder Regularity for Kinetic Fokker--Planck Equations with General Transport Operators and Rough Coefficients ⋮ Global regularity estimates for the Boltzmann equation without cut-off

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularizing effect and local existence for the non-cutoff Boltzmann equation
• Fractional diffusion limit for collisional kinetic equations
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Fractional kinetic equation for Hamiltonian chaos
• Regularity of the moments of the solution of a transport equation
• \(L^ p\) regularity of velocity averages
• Hypoelliptic regularity in kinetic equations.
• Local existence, lower mass bounds, and a new continuation criterion for the Landau equation
• Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials
• De Giorgi techniques applied to Hamilton-Jacobi equations with unbounded right-hand side
• The Schauder estimate in kinetic theory with application to a toy nonlinear model
• The weak Harnack inequality for the Boltzmann equation without cut-off
• \(C^\infty\) smoothing for weak solutions of the inhomogeneous Landau equation
• Hypoellipticity for a class of kinetic equations
• Hypoelliptic second order differential equations
• The averaging lemma
• On Some Pointwise Inequalities Involving Nonlocal Operators
• Fractional diffusion limit for collisional kinetic equations: A moments method
• Regularity theory for parabolic nonlinear integral operators
• Régularité $L\sp p$ précisée des moyennes dans les équations de transport
• Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation
• Harnack inequalities for non-local operators of variable order
• Hypoelliptic Estimates for a Linear Model of the Boltzmann Equation Without Angular Cutoff
• Global hypoelliptic estimates for fractional order kinetic equation
• The fractional kinetic equation and thermonuclear functions.

This page was built for publication: Hölder Continuity for a Family of Nonlocal Hypoelliptic Kinetic Equations