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