Complex potentials with logarithmic singularities in kernels for elastic bodies with defect along a smooth arc (Q1603104)

The authors construct integral representation with logarithmic singularity in kernel for functions analytic in different domains of complex plane with cuts along a smooth arc. Elastic plane with defect along a smooth arc, half-plane with defect along an arc, elastic disc with defect along a smooth arc, and domains conformally equivalent to disc are considered. Singularities (poles) of potentials are analyzed. Numerical solutions are not considered.