The harmonic Dirichlet problem in a planar domain with cracks
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...
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Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
2008-11-01
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| Series: | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| Online Access: | http://studmath.up.krakow.pl/index.php/studmath/article/view/82 |
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Article |
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doaj-14edb152be144dba9815bf72cd54d6792020-11-24T23:08:58ZdeuWydawnictwo Naukowe Uniwersytetu PedagogicznegoAnnales Universitatis Paedagogicae Cracoviensis: Studia Mathematica 2081-545X2008-11-0171113123The harmonic Dirichlet problem in a planar domain with cracksP. A. KrutitskiiN. Ch. KrutitskayaThe 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.http://studmath.up.krakow.pl/index.php/studmath/article/view/82 |
| collection |
DOAJ |
| language |
deu |
| format |
Article |
| sources |
DOAJ |
| author |
P. A. Krutitskii N. Ch. Krutitskaya |
| spellingShingle |
P. A. Krutitskii N. Ch. Krutitskaya The harmonic Dirichlet problem in a planar domain with cracks Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| author_facet |
P. A. Krutitskii N. Ch. Krutitskaya |
| author_sort |
P. A. Krutitskii |
| title |
The harmonic Dirichlet problem in a planar domain with cracks |
| title_short |
The harmonic Dirichlet problem in a planar domain with cracks |
| title_full |
The harmonic Dirichlet problem in a planar domain with cracks |
| title_fullStr |
The harmonic Dirichlet problem in a planar domain with cracks |
| title_full_unstemmed |
The harmonic Dirichlet problem in a planar domain with cracks |
| title_sort |
harmonic dirichlet problem in a planar domain with cracks |
| publisher |
Wydawnictwo Naukowe Uniwersytetu Pedagogicznego |
| series |
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| issn |
2081-545X |
| publishDate |
2008-11-01 |
| description |
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. |
| url |
http://studmath.up.krakow.pl/index.php/studmath/article/view/82 |
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