Preprint no. 147
Mathematical Institute of the Academy of Sciences of the Czech Republic

The harmonic Dirichlet problem for cracked domain with jump conditions on cracks

Pavel Krutitskii, Dagmar Medkova

Pavel Krutitskii, Department of Mathematics, Faculty of Physics, Moscow State University, Moscow 117234, Russia, e-mail: krutitsk@math380b.phys.msu.su ; Dagmar Medkova, Mathematical Institute, Acad. Sci.of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: medkova@math.cas.cz

Summary: The harmonic problem in a cracked domain is studied in $R^m$, $m>2$. The boundary of the domain is assumed to be nonsmooth, while cracks are smooth. The Dirichlet condition is specified on the boundary of the domain and jumps of the unknown function and its normal derivative is specified on the cracks. Uniqueness and solvability results are obtained. The problem is reduced to the uniquely solvable integral equation.

Keywords: Laplace equation, crack, single layer potential, double layer potential

MSC (2000) Subject Classification: 31B10, 35J05

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