Spectral relationships of the integral equation with logarithmic kernel in some different domains

In this work, the Fredholm integral equation (FIE) with logarithmic kernel is investigated from the contact problem in the plane theory of elasticity. Then, using potential theory method (PTM), the spectral relationships (SRs) of this integral equation are obtained in some different domains of the contact. Many special cases and new SRs are established and discussed from this work.