analytic function, complex potential, Dirichlet problem

The paper develops a stochastic theory-building in connection with its application to the solution of basic problems of the theory of elasticity. Particular attention is paid to the Dirichlet problem for N analytic functions. The relevance of the research topic is related to the fact that the theory of stochastic boundary value problems in the class of N analytic functions being formed. In the work is given an exact mathematical formulation of stochastic Dirichlet problem for N is an analytic function. It develops the necessary mathematical apparatus. A theorem on the existence and uniqueness of solutions. Get a general algorithm for solving stochastic Dirichlet problem for a fairly wide class of regions and contours, its stability is investigated. We give an example of the first major decisions of the elasticity problem with the use of stochastic Dirichlet problem for the n-analytic functions. In the study we used the theory of boundary value problems for analytic functions and bianalytic, X-boundary properties of analytic functions, properties of stochastic differential systems.

Maximova Lyudmila Anatolievna e-mail: maximova_ng@mail.ru, Doctor of Physics and Mathematics, Professor, Chuvash State University, Cheboksary, Russia; I. Yakovlev Chuvash State Pedagogical University, Cheboksary, Russia.

Yudenkov Alexey Vitalevich, Doctor of Physics and Mathematics, Professor, Smolensk State Agricultural Academy, Smolensk, Russia.