Nonlinear potential analysis on Morrey spaces and their capacities

Abstract

To study the existence and regularity, even just partial regularity (smoothness except for a closed exceptional set of some measure or capacity zero) for higher order (nonlinear) elliptic equations (systems), we intend to develop a nonlinear potential analysis on Morrey spaces, fractional Riesz potentials, fractional maximal functions, and Morrey capacities of two different types.