On an Elliptic Problem in a Half-Planewith a Cut along a Ray

We investigate the solvability in the Sobolev–Slobodetskii space of a model elliptic pseudodifferential equation in a plane domain that is a union of two quadrants. Using the concept of wave factorization of an elliptic symbol, it is possible to write out a general solution to this equation, to which, in a special case, the Dirichlet and Neumann conditions are added on the domain boundary. The resulting boundary value problem is reduced to an equivalent system of linear integral equations.