An extremal problem for Laplace's equation in a half-space

The use of a minimum condition for a given functional to determine a function harmonic in a half-space whose boundary value is given only on part of the boundary plane is reduced to one or more Dirichlet problems for plane regions. The functional is defined as the L₂-distance between the limiting values of the normal derivative of the harmonic function and a given function.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 101–103.