| 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. |
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