A Contact Problem for a Half-Space and a Rigid Base with an Axially Symmetric Recess

An axially symmetric problem of frictionless contact interaction of an elastic half-space and a rigid base that has a small surface recess is considered. A corresponding problem of elasticity theory is formulated. The problem is solved by the method of double integral equations. The contact pressure, the surface shape of the half-space after compression, and the size of the gap are found in closed form.