Ein Kapazitätsbegriff für gewichtete Sobolewräume

Abstract

A capacity for weighted Sobolev spaces $H^1(g)$ is introduced. The thinnes of a set in a point is defined. It is proved, that functions from $H^1(g)$ may be understood as precisely defined functions and that they are finely continuous quasi everywhere. For every set with finite capacity there exists a capacitary potential.