M. Basheleishvili

The Investigation of the Fourth Boundary Value Problem for Equations of Statics of Elastic Mixture for a Circle and an Infinite Plane with a Circular Hole

abstract:
The fourth boundary value problem for a circle and for an infinite domain with a circular hole is formulated. The theorem on the uniqueness of a solution is proved. Singular integral equations with Hilbert kernel are obtained for solving the problems. The formula of permutation of singular integrals with Hilbert kernel is used. The solutions of the above-mentioned
problems are represented in terms of the Poisson formula.

Mathematics Subject Classification: 74B05

Key words and phrases: Singular integral equations with Hilbert kernel, potentials, Fredholm equations, Green's formula