2 citations · 3 across the 13 of their papers we have counts for
13 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 bo…
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 .…
Higher regularity in nonlocal free boundary problems
Begoña Barrios, Xavier Ros-Oton, Marvin Weidner
We study the higher regularity in nonlocal free boundary problems posed for general integro-differential operators of order . Our main result is for the nonlocal one-phase (Ber…
Optimal regularity for kinetic Fokker-Planck equations in domains
Xavier Ros-Oton, Marvin Weidner
We study the smoothness of solutions to linear kinetic Fokker-Planck equations in domains with specular reflection condition, including Kolmogorov's equatio…
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^…
Regularity for the Boltzmann equation conditional to pressure and moment bounds
Xavier Fernández-Real, Xavier Ros-Oton, Marvin Weidner
We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in $L…
Improvement of flatness for nonlocal free boundary problems
Xavier Ros-Oton, Marvin Weidner
In this article we study for the first time the regularity of the free boundary in the one-phase free boundary problem driven by a general nonlocal operator. Our main results estab…
Optimal regularity for nonlocal elliptic equations and free boundary problems
Xavier Ros-Oton, Marvin Weidner
In this article we establish for the first time the boundary regularity of solutions to nonlocal elliptic equations with kernels . This was known to h…
Regularity for nonlocal equations with local Neumann boundary conditions
Xavier Ros-Oton, Marvin Weidner
In this article we establish fine results on the boundary behavior of solutions to nonlocal equations in domains which satisfy local Neumann conditions on the boundary. S…
Potential theory for nonlocal drift-diffusion equations
Quoc-Hung Nguyen, Simon Nowak, Yannick Sire +1
The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion equations via pointwise potential estimates. Our analysis requires only minimal assum…