SPECIAL INTEGRAL-EQUATIONS OF POTENTIAL-THEORY

Special integral equations are proposed for the Dirichlet problem on a system of open contours and the mixed boundary-value problem. For a two-dimensional elliptic differential operator of second order. It is shown that the corresponding integral operators are selfadjoint and positive relative to a suitably defined scalar product. A numerical method is proposed for solving the integral equations, based on the use of adaptive grids.