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Fine behaviour of solutions of the Dirichlet problem near an irregular point. (English) Zbl 0699.31015
The behaviour of the generalized solution $$H^ uf$$ of the Dirichlet problem, on a bounded open set u with resolutive boundary data f, is investigated near an irregular boundary point z. Since z is irregular, $$H^ uf(y)$$ may not have a limit as y approaches z. However, if f is lower bounded, then $$H^ uf$$ has a fine limit and the author shows that this limit is equal to the integral of f with respect to the balayage of the Dirac measure.
Reviewer: P.M.Gauthier

##### MSC:
 31B25 Boundary behavior of harmonic functions in higher dimensions 31D05 Axiomatic potential theory 31B35 Connections of harmonic functions with differential equations in higher dimensions