Mixed boundary value problem in Potential Theory: Application to the hydrodynamic impact (Wagner) problem

A three-dimensional solution of the mixed boundary value problem posed in Potential Theory is proposed. The support of the Neumann condition is conformally mapped onto a unit disk. On that disk, the solution is broken down as Fourier series of azimuthal angle and linear combinations of known functions of the radial coordinate. It is shown that the whole problem reduces highly nonlinear equations for the coefficients of the mapping function. The present method of solution is to be applied to hydrodynamic impact problem.