We present some properties of a nonlocal version of the Neumann boundary conditions associated to problems involving the fractional p-Laplacian. For this problems, we show some regularity results for the general case and some existence results for particular types of problems. When p=2, we give a generalization of the boundary conditions in which both the nonlocal and the classic Neumann conditions are present, and we consider problems involving both nonlocal and local interactions.

Bruno Pini Mathematical Analysis Seminar, Vol. 14 No. 1 (2023): Nonlocal and Nonlinear PDEs at the University of Bologna