On one problem of the plane theory of elasticity for a circular domain with a rectangular hole

The paper considers a plane problem of elasticity for a circle with a rectangular hole. To find a solution, the use is made both of the method of conformal mappings and of boundary value problems of analytic functions. In particular, relying on the well-known Kolosov–Muskhelishvili’s formulas, the problem formulated with respect to unknown complex potentials is reduced to the two Riemann–Hilbert problems for a circular ring, and the solutions of the latter problems allow us to construct potentials effectively (analytically). The estimates of the obtained results in the neighborhood of angular points are given. Analogous results (as a particular case) are obtained for a circular domain with a rectilinear cut.