Regularity theory for nonlocal equations

 

Nonlocal equations, often modeled using the fractional Laplacian, have received significant attention in recent years. In this talk, we will briefly overview how the classical regularity theory for second-order (elliptic) PDEs (in divergence form) has been extended to fractional-order nonlocal equations. We will explore the Schauder, De Giorgi–Nash–Moser, Morrey–Campanato, and Calderón–Zygmund theories, and present some open problems in these fields.