The harmonic problem in the plane with cuts under boundary conditions of the third kind (Q960666)

This is an announcement of results of the author concerning the boundary value problem for harmonic functions on the plane with a finite number of cuts along simple open arcs of certain smoothness. For third kind boundary conditions on both sides of the cuts existence and uniqueness of the solution is stated. Furthermore, an integral representation of the solution as potentials whose density is determined from a uniquely solvable system of integral equations is provided. The singularities of the gradient of the solution at the endpoints of the cuts are also studied.