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Zeitschrift für Analysis und ihre Anwendungen

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Volume 2, Issue 3, 1983, pp. 273–280
DOI: 10.4171/ZAA/64

Published online: 1983-06-30

Ein Kapazitätsbegriff für gewichtete Sobolewräume

Ehrhard Herbst[1]

(1) Universität Rostock, Germany

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.

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Herbst Ehrhard: Ein Kapazitätsbegriff für gewichtete Sobolewräume. Z. Anal. Anwend. 2 (1983), 273-280. doi: 10.4171/ZAA/64