11 papers
Kinetic Fokker-Planck equations with Maxwell boundary conditions
Kyeongbae Kim, Marvin Weidner
We develop the boundary regularity theory for solutions to linear kinetic Fokker-Planck equations with Maxwell boundary conditions. These conditions interpolate between diffuse and…
Boundary Harnack estimates of optimal order for kinetic Fokker-Planck equations
Kyeongbae Kim, Marvin Weidner
We establish higher order boundary Harnack estimates for solutions to kinetic Fokker-Planck equations with absorbing incoming boundaries. Unlike classical elliptic and parabolic eq…
Sharp regularity near the grazing set for kinetic Fokker-Planck equations
Kyeongbae Kim, Marvin Weidner
We prove optimal regularity results for solutions to linear kinetic Fokker-Planck equations in bounded domains. Our contributions are two-fold. First, we establish the sharp $C^{1/…
Dirichlet heat kernel estimates for parabolic nonlocal equations
Philipp Svinger, Marvin Weidner
In this article we establish the optimal boundary regularity for solutions to nonlocal parabolic equations in divergence form in domains and prove a higher order b…
The Neumann problem for the fractional Laplacian: optimal regularity via the Mellin transform
Serena Dipierro, Xavier Ros-Oton, Enrico Valdinoci +1
We establish the optimal regularity of solutions to the Neumann problem for the fractional Laplacian, in , with the external condition in $Ω^c…
Optimal boundary regularity and Green function estimates for nonlocal equations in divergence form
Minhyun Kim, Marvin Weidner
In this article we prove for the first time the boundary regularity for solutions to nonlocal elliptic equations with Hölder continuous coefficients in divergence form in $C…