The method of integral equations for the mixed problem with the skew derivative for harmonic functions outside cuts in a plane

We consider the mixed problem for Laplace's equation outside cuts in a plane. The Dirichlet boundary condition is posed on one side of each cut, and the skew derivative condition is posed on the other side. This problem generalizes the mixed Dirichlet–Neumann problem. Using the method of potentials, this problem is reduced to a uniquely solvable Fredholm integral equation of the second kind.