Special Session 48: Recent Advances in Nonlinear PDEs and Inverse Problems

Boundary regularity for nonlocal equations
Marvin Weidner
University of Bonn
Germany
Co-Author(s):    Serena Dipierro, Xavier Ros-Oton, Enrico Valdinoci
Abstract:
The boundary behavior for solutions to nonlocal equations with exterior Dirichlet boundary conditions has been extensively studied in recent years and it is well known that, in general, s-harmonic functions are not better than $C^s$. In contrast, the Neumann problem for nonlocal equations has received much less attention, and the optimal boundary regularity of solutions remains unknown. In this talk, I will present recent progress on this question, based on a new classification result for solutions to general nonlocal equations in 1D. This is joint work with Serena Dipierro, Xavier Ros-Oton, and Enrico Valdinoci.