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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | deu |
| Published: |
Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
2008-11-01
|
| Series: | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| Online Access: | http://studmath.up.krakow.pl/index.php/studmath/article/view/82 |
| Summary: | 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. |
|---|---|
| ISSN: | 2081-545X |