Netuka, Ivan Fine behaviour of solutions of the Dirichlet problem near an irregular point. (English) Zbl 0699.31015 Bull. Sci. Math., II. Sér. 114, No. 1, 1-22 (1990). 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 Cited in 1 ReviewCited in 2 Documents 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 Keywords:Dirichlet problem; irregular boundary point; fine limit; balayage PDF BibTeX XML Cite \textit{I. Netuka}, Bull. Sci. Math., II. Sér. 114, No. 1, 1--22 (1990; Zbl 0699.31015)