12 citations · 23 across the 10 of their papers we have counts for
10 papers
Stationary kinetic Krylov-Safonov estimates in space dimension one
Yuzhe Zhu
We prove interior Hölder regularity for solutions of the stationary kinetic Fokker-Planck equation in non-divergence form in space dimension one. The estimate is independent of any…
Fisher information for the multi-species Landau system
Yuzhe Zhu
We consider the Fisher information for spatially homogeneous multi-species Landau system. We show that the mass-weighted Fisher information is monotone decreasing in time along the…
Sharp boundary regularity properties for hypoelliptic kinetic equations
Yuzhe Zhu
We establish sharp boundary regularity results for solutions to kinetic Fokker-Planck equations under prescribed inflow boundary conditions, providing precise quantification of the…
On the Fermi-Dirac-type Fisher information
Yuzhe Zhu
We consider kinetic models for Fermi-Dirac-like particles obeying the exclusion principle. A generalized notion of Fisher information, tailored to kinetic equations of Fermi-Dirac-…
Averaging lemmas and hypoellipticity
Yuzhe Zhu
We use the methods of commutator and fundamental solutions to establish averaging lemmas and hypoelliptic estimates for purely kinetic transport equations. Assuming certain amount…
A note on asymptotics of linear dissipative kinetic equations in bounded domains
Yuzhe Zhu
We establish -exponential decay properties for linear dissipative kinetic equations, including the time-relaxation and Fokker-Planck models, in bounded spatial domains with ge…
Propagation of smallness for solutions of elliptic equations in the plane
Yuzhe Zhu
We explore quantitative propagation of smallness for solutions of two-dimensional elliptic equations from sets of positive -dimensional Hausdorff content for any . In parti…
Regularity of kinetic Fokker-Planck equations in bounded domains
Yuzhe Zhu
We obtain the existence, uniqueness and regularity results for solutions to kinetic Fokker-Planck equations with bounded measurable coefficients in the presence of boundary conditi…
On a spatially inhomogeneous nonlinear Fokker-Planck equation: Cauchy problem and diffusion asymptotics
Francesca Anceschi, Yuzhe Zhu
We investigate the Cauchy problem and the diffusion asymptotics for a spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck operator. We derive the global w…
Velocity averaging and Hölder regularity for kinetic Fokker-Planck equations with general transport operators and rough coefficients
Yuzhe Zhu
This article addresses the local boundedness and Hölder continuity of weak solutions to kinetic Fokker-Planck equations with general transport operators and rough coefficients. The…