ON THE MIXED PROBLEM FOR LAPLACE EQUATION OUTSIDE CUTS, PLACED ALONG A CIRCUMFERENCE IN A PLANE

The boundary value problem for harmonic functions outside cuts lying on the arcs of a circumference is considered. The Dirichlet condition is given on one side of each cut and Neumann condition is specified on the other side. The problem is reduced to the Riemann-Hilbert problem for complex analytic function, which is solved in a closed form. An explicit solution of the original problem is obtained.