Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation
From MaRDI portal
Publication:4633460
DOI10.2422/2036-2145.201702_001zbMath1431.35016arXiv1607.08068OpenAlexW2963822970MaRDI QIDQ4633460
Clément Mouhot, Cyril Imbert, Alexis F. Vasseur, François Golse
Publication date: 2 May 2019
Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1607.08068
Smoothness and regularity of solutions to PDEs (35B65) Hypoelliptic equations (35H10) Fokker-Planck equations (35Q84)
Related Items (76)
The Dirichlet problem for Kolmogorov-Fokker-Planck type equations with rough coefficients ⋮ Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations ⋮ An \(L^2\) to \(L^\infty\) framework for the Landau equation ⋮ A probabilistic study of the kinetic Fokker-Planck equation in cylindrical domains ⋮ About the Landau-Fermi-Dirac equation with moderately soft potentials ⋮ Enhanced dissipation and Hörmander's hypoellipticity ⋮ Partial Regularity in Time for the Space-Homogeneous Landau equation with Coulomb Potential ⋮ Spatial regularity for a class of degenerate Kolmogorov equations ⋮ Global \({L}_p\) estimates for kinetic Kolmogorov-Fokker-Planck equations in nondivergence form ⋮ Quantitative De Giorgi methods in kinetic theory ⋮ Asymptotics toward viscous contact waves for solutions of the Landau equation ⋮ Hardy-Littlewood-Sobolev inequalities for a class of non-symmetric and non-doubling hypoelliptic semigroups ⋮ Regularity for the Boltzmann equation conditional to macroscopic bounds ⋮ Existence of a fundamental solution of partial differential equations associated to Asian options ⋮ Quantitative spectral gaps for hypoelliptic stochastic differential equations with small noise ⋮ Harnack inequality for a class of Kolmogorov-Fokker-Planck equations in non-divergence form ⋮ LOG-TRANSFORM AND THE WEAK HARNACK INEQUALITY FOR KINETIC FOKKER-PLANCK EQUATIONS ⋮ Entropy dissipation estimates for the relativistic Landau equation, and applications ⋮ Unconditional Regularity and Trace Results for the Isentropic Euler Equations with \({\boldsymbol{\gamma = 3}}\) ⋮ De Giorgi argument for weighted \(L^2\cap L^{\infty}\) solutions to the non-cutoff Boltzmann equation ⋮ Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials ⋮ Small Knudsen rate of convergence to contact wave for the Landau equation ⋮ Sobolev embeddings for kinetic Fokker-Planck equations ⋮ Analytic Gelfand-Shilov smoothing effect of the spatially homogeneous Landau equation with hard potentials ⋮ Weak and Renormalized Solutions to a Hypoelliptic Mean Field Games System ⋮ 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 ⋮ Gaussian Bounds for the Inhomogeneous Landau Equation with Hard Potentials ⋮ On the fundamental solution for degenerate Kolmogorov equations with rough coefficients ⋮ A structure theorem for elliptic and parabolic operators with applications to homogenization of operators of Kolmogorov type ⋮ Quantitative De Giorgi methods in kinetic theory for non-local operators ⋮ The Vlasov–Poisson–Boltzmann/Landau System with Polynomial Perturbation Near Maxwellian ⋮ Regularity estimates and open problems in kinetic equations ⋮ Stability of vacuum for the Landau equation with hard potentials ⋮ 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 ⋮ On a spatially inhomogeneous nonlinear Fokker-Planck equation: Cauchy problem and diffusion asymptotics ⋮ Lower bounds on the Lyapunov exponents of stochastic differential equations ⋮ Global \(\boldsymbol{L}_{\boldsymbol{p}}\) Estimates for Kinetic Kolmogorov–Fokker–Planck Equations in Divergence Form ⋮ Pencil-Beam Approximation of Stationary Fokker--Planck ⋮ Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules ⋮ Local solutions of the Landau equation with rough, slowly decaying initial data ⋮ Unnamed Item ⋮ Compactness properties and local existence of weak solutions to the Landau equation ⋮ Topologically Based Fractional Diffusion and Emergent Dynamics with Short-Range Interactions ⋮ Gaussian Lower Bounds for the Boltzmann Equation without Cutoff ⋮ The Fokker--Planck Equation with Absorbing Boundary Conditions in Bounded Domains ⋮ Stability, well-posedness and regularity of the homogeneous Landau equation for hard potentials ⋮ A Compactness Result for the Sobolev Embedding via Potential Theory ⋮ Kinetic maximal \(L_\mu^p(L^p)\)-regularity for the fractional Kolmogorov equation with variable density ⋮ The Landau equation with the specular reflection boundary condition ⋮ Functional inequalities for a class of nonlocal hypoelliptic equations of Hörmander type ⋮ Stability of vacuum for the Landau equation with moderately soft potentials ⋮ Gaussian lower bounds for non-homogeneous Kolmogorov equations with measurable coefficients ⋮ Small Knudsen rate of convergence to rarefaction wave for the Landau equation ⋮ Hölder Continuity for a Family of Nonlocal Hypoelliptic Kinetic Equations ⋮ The Schauder estimate for kinetic integral equations ⋮ On the fine properties of parabolic measures associated to strongly degenerate parabolic operators of Kolmogorov type ⋮ Kinetic maximal \(L^p\)-regularity with temporal weights and application to quasilinear kinetic diffusion equations ⋮ Controllability of some collisional and non-collisional kinetic equations: Fokker-Planck and Vlasov-Navier-Stokes ⋮ Quantitative parabolic regularity à la De Giorgi ⋮ \(C^\infty\) smoothing for weak solutions of the inhomogeneous Landau equation ⋮ Uniqueness of bounded solutions for the homogeneous relativistic Landau equation with Coulomb interactions ⋮ Kinetic maximal \(L^2\)-regularity for the (fractional) Kolmogorov equation ⋮ Potential theory for a class of strongly degenerate parabolic operators of Kolmogorov type with rough coefficients ⋮ Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation ⋮ A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations ⋮ A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients ⋮ Velocity Averaging and Hölder Regularity for Kinetic Fokker--Planck Equations with General Transport Operators and Rough Coefficients ⋮ The Schauder estimate in kinetic theory with application to a toy nonlinear model ⋮ Local conditional regularity for the Landau equation with Coulomb potential ⋮ Decay estimates for large velocities in the Boltzmann equation without cutoff ⋮ Global regularity estimates for the Boltzmann equation without cut-off ⋮ A note on the weak regularity theory for degenerate Kolmogorov equations ⋮ The Vlasov-Poisson-Landau system with the specular-reflection boundary condition ⋮ The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off
This page was built for publication: Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation
