%0 Journal Article
%T The harmonic Dirichlet problem in a planar domain with cracks
%A P. A. Krutitskii
%A N. Ch. Krutitskaya
%J Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
%D 2008
%I Krak¨®w : Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
%X 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.
%U http://studmath.up.krakow.pl/index.php/studmath/article/view/82