Contact of two half spaces one of which contains a ring-shaped pit. Part 1. Singular integral equation

We consider an axisymmetric problem of elastic contact of two half spaces one of which contains a ring-shaped pit. A method proposed for the solution of this problem is based on the construction of a special integral representation of the components of the vector of displacements and stress tensor via the height of the gap with subsequent reduction of the original problem to the solution of a singular integral equation with leading singularity of the Cauchy type relative to the derivative of the height of the gap.