Boundary value problem for the Helmholtz equation outside cuts on the plane with boundary conditions of the third kind (Q946105)

The boundary value problem for the Helmholtz equation is investigated outside cuts on the plane in which a boundary condition of the third kind is posed on both sides of the cuts. The author proves existence and uniqueness theorems for this problem. For this purpose integral representations of the solution are obtained in the form of potential, and a vector Fredholm equation of the second kind is derived, which is uniquely solvable in a certain Banach space.