Nonlocal Neumann boundary conditions

Abstract

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.

Keywords

• fractional p-laplacian
• neumann boundary conditions
• regularity
• superlinear problems
• mixed local and fractional laplacians