The harmonic Dirichlet problem in a planar domain with cracks

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Author:
Krutitskii, P.A.
Krutitskaya, N.Ch.
xmlui.dri2xhtml.METS-1.0.item-citation: Annales Academiae Paedagogicae Cracoviensis. 63, Studia Mathematica 7 (2008), s. [113]-123
xmlui.dri2xhtml.METS-1.0.item-iso: en
Date: 2008
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Dokument cyfrowy wytworzony, opracowany, opublikowany oraz finansowany w ramach programu "Społeczna Odpowiedzialność Nauki" - modułu "Wsparcie dla bibliotek naukowych" przez Ministerstwo Nauki i Szkolnictwa Wyższego w projekcie nr rej. SONB/SP/465103/2020 pt. "Organizacja kolekcji czasopism naukowych w Repozytorium UP wraz z wykonaniem rekordów analitycznych".
Abstract
The harmonic Dirichlet problem in a planar domain with smooth cracks of an arbitrary shape is considered in case, when the solution is not continuous at the ends of the cracks. The well-posed formulation of the problem is given, theorems on existence and uniqueness of a classical solution are proved, the integral representation for a solution is obtained. With the help of the integral representation, the properties of the solution are studied. It is proved that a weak solution of the Dirichlet problem in question does not typically exist, though the classical solution exists.
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http://hdl.handle.net/11716/9952
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