The jump problem for the Helmholtz equation and singularities at the edges Original Research Article

The boundary value problem for the Helmholtz equation outside several cuts in a plane is studied. The jump of the solution of the Helmholtz equation and the jump of its normal derivative are specified of the cuts. The unique solution of this problem is constructed in the explicit form by means of single layer and angular potentials. The singularities at the ends of the cuts are investigated.