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Angular limits of double layer potentials. (English) Zbl 0838.31006
The double layer potential on a Borel set $$A \subset \mathbb{R}^n$$ and angular limits of the double layer potential are investigated under very general assumptions. Given $$\eta \in \partial A$$ it is supposed that $$G = \mathbb{R}^n \backslash A$$ has locally finite perimeter in $$\mathbb{R}^n \backslash \{\eta\}$$. Let $$q : \partial A \to \langle 0, + \infty \rangle$$ be a lower-semicontinuous function which is bounded and strictly positive on $$\partial A \backslash \{\eta\}$$. Some necessary and sufficient geometric conditions are given for the existence of angular limits in $$\eta$$ of the double layer potential with any continuous density $$f : \partial A \to \mathbb{R}$$ such that $f(\xi) - f(\eta) = o \bigl( q(\xi) \bigr) \quad \text{as} \quad \xi \to \eta,\quad \xi \in \partial A.$
Reviewer: M.Dont (Praha)

##### MSC:
 31B25 Boundary behavior of harmonic functions in higher dimensions
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##### References:
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