Quantitative De Giorgi methods in kinetic theory

DOI10.5802/jep.203zbMath1495.35109arXiv2103.09646OpenAlexW3136689319MaRDI QIDQ2154282

Jessica Guerand, Clément Mouhot

Publication date: 19 July 2022

Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.09646

zbMATH Keywords

trajectoriesFokker-Planck equationHölder continuitykinetic theoryKolmogorov equationweak Harnack inequalityMoser iterationultraparabolic equationshypoelliptic equationsaveraging lemmaDe Giorgi method

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) Ultraparabolic equations, pseudoparabolic equations, etc. (35K70) Integro-partial differential equations (35R09) Fokker-Planck equations (35Q84)

Related Items (10)

LOG-TRANSFORM AND THE WEAK HARNACK INEQUALITY FOR KINETIC FOKKER-PLANCK EQUATIONS ⋮ Unconditional Regularity and Trace Results for the Isentropic Euler Equations with \({\boldsymbol{\gamma = 3}}\) ⋮ Calculus of variations. Abstracts from the workshop held August 14--20, 2022 ⋮ \(C^\alpha\) regularity of weak solutions of non-homogeneous ultraparabolic equations with drift terms ⋮ On the fundamental solution for degenerate Kolmogorov equations with rough coefficients ⋮ Quantitative De Giorgi methods in kinetic theory for non-local operators ⋮ On regularity and existence of weak solutions to nonlinear Kolmogorov-Fokker-Planck type equations with rough coefficients ⋮ Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation ⋮ Unnamed Item ⋮ A note on the weak regularity theory for degenerate Kolmogorov equations

Cites Work

• The \(C^{\alpha}\) regularity of weak solutions of ultraparabolic equations
• The \(C^{\alpha}\) regularity of a class of non-homogeneous ultraparabolic equations
• Zufällige Bewegungen. (Zur Theorie der Brownschen Bewegung.)
• Quantitative parabolic regularity à la De Giorgi
• Hypocoercivity without confinement
• The weak Harnack inequality for the Boltzmann equation without cut-off
• Hypoelliptic second order differential equations
• A note on the Harnack inequality for elliptic equations in divergence form
• Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation
• A survey on the classical theory for Kolmogorov equation
• THE MOSER'S ITERATIVE METHOD FOR A CLASS OF ULTRAPARABOLIC EQUATIONS
• A harnack inequality for parabolic differential equations
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