The method of transformation operators as applied to vector boundary value problems

The method of transformation operators has been applied to the several vector boundary value problems. Transformation operators for every harmonic function in the half-space and in the ball were identified for the Robin problems for a homogenous half-space and for a homogenous m-dimensional ball, respectively. The fourth boundary value problem in a ball was also described with a separate system of Laplace equations with specific boundary condition and the compatibility conditions. The transformation operator was also expressed for the inverse Dirichlet problem for a piecewise homogenous ball to determine boundary values of a harmonic function in the ball from the given values of this function on the sphere.