Abstract
As an application of balayage theory we shall study various types of the Dirichlet problem in balayage spaces. The properties of Perron sets (section 1) permit to develop the generalized solution of the Dirichlet problem for open sets U by the method of Perron, Wiener, and Brelot (section 2). It turns out that this solution recovers the harmonic kernels HU . The boundary behavior of the generalized solution is investigated in sections 3 and 4 leading among others to well known classical theorems.
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© 1986 Springer-Verlag Berlin Heidelberg
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Bliedtner, J., Hansen, W. (1986). Dirichlet Problem. In: Potential Theory. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71131-2_8
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DOI: https://doi.org/10.1007/978-3-642-71131-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16396-1
Online ISBN: 978-3-642-71131-2
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