For the Helmholtz equation outside cuts in a plane a boundary-value problem is studied. The Dirichlet condition is specified on one side of each cut and the Neumann condition, on its other side. The existence and uniqueness theorems for the solution of the boundary-value problem are proved. An integral representation for the solution is obtained in the form of potentials. From a uniquely solvable system of integral equations, the density in the potentials is determined.
Department of Mathematics, Department of Solid-State Physics, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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