Stabilized approximate solutions of certain integral equations of first kind arising in contact problems of elasticity

Abstract

The paper presents a method of constructing, by successive approximation, stabilized approximate solutions of certain integral equations of first kind in contact problems of elasticity. In these equations, the unknown function is a surface stress under the stamp, which is allowed to have a square root singularity under the edges of the stamp, and is therefore not square integrable. The author shows that it is nevertheless possible to apply the theory of positive operators to the present problem by constructing an appropriate L2-space which includes functions with square root singularities. © 1984 Martinus Nijhoff Publishers.