A capacity for weighted Sobolev spaces is introduced. The thinnes of a set in a point is defined. It is proved, that functions from 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.
Cite this article
Ehrhard Herbst, Ein Kapazitätsbegriff für gewichtete Sobolewräume. Z. Anal. Anwend. 2 (1983), no. 3, pp. 273–280DOI 10.4171/ZAA/64