Capacities

Abstract

Capacities are needed to understand point-wise behavior of Sobolev functions. They also play an important role in studies of solutions of partial differential equations. In this chapter we study two kinds of capacities: Sobolev capacity in Sect. 10.1 and relative capacity in Sect. 10.2. Both capacities have their advantages. The Sobolev capacity is independent of the underlying set, but extremal functions are difficult to find.