A detour on a class of nonlocal degenerate operators

Abstract

We present some recent results on a class of degenerate operators which are modeled on the fractional Laplacian, converge to the truncated Laplacian, and are extremal among operators with fractional diffusion along subspaces of possibly different dimensions. In particular, we will recall basic properties of these operators, validity of maximum principles, and related phenomena.

Keywords

• maximum and comparison principles
• fully nonlinear degenerate elliptic pde
• nonlocal operators
• eigenvalue problem