5 papers · 1 filter
Capacitary estimates for solutions to nonlocal Dirichlet problems
Minhyun Kim, Se-Chan Lee, Marvin Weidner
We study the boundary regularity of weak solutions to nonlocal nonlinear elliptic equations with bounded measurable coefficients. Our main result establishes that a capacity densit…
Nonnegative solutions to nonlocal parabolic equations
Naian Liao, Marvin Weidner
We aim to study nonnegative, global solutions to a general class of nonlocal parabolic equations with bounded measurable coefficients. First, we prove a Widder-type theorem. Such a…
Time-insensitive nonlocal parabolic Harnack estimates
Naian Liao, Marvin Weidner
We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal…
The Harnack inequality fails for nonlocal kinetic equations
Moritz Kassmann, Marvin Weidner
We prove that the Harnack inequality fails for nonlocal kinetic equations. Such equations arise as linearized models for the Boltzmann equation without cutoff and are of hypoellipt…
Semiconvexity estimates for nonlinear integro-differential equations
Xavier Ros-Oton, Clara Torres-Latorre, Marvin Weidner
In this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro-differential operators with ge…