გურამ ქუთათელაძე

For a plane with rectilinear cuts lying along the segments of two mutually perpendicular straight lines we consider the problem on finding two piecewise holomorphic functions when in the boundary conditions for the cuts to the given value of the first function is added the conjugate value of the second one. The solution of the problem is constructed in two modes in the classes of N.Muskhelishvili, explicitly (in a closed form), by the Cauchy type integrals.

For multiply-connected domains of special type, i.e. for a plane and a half-plane with cuts, we consider boundary value problems of finding two piecewise holomorphic functions, when on the boundary of the domain to the given value of the first function the conjugate value of the second function is added. Solutions are constructed, in a closed form, in the Cauchy type integrals.

The question of numerical realisation of solution of some boundary problems concerning appendices of a known problem of conjugate of the theory of holomorph functions is considered. In this case the corresponding problem is concretized in the form of a certain class of problems of the theory of elasticity for an infinite plane with the focused rectilinear cuts.