Integral Equations with Logarithmic Kernels

A consolidated account is presented of the singular integral equations with logarithmic kernels which occur very frequently in applied mathematics. The analysis starts with the simplest integral equation of this type and progresses steadily to more complicated ones. The Fredholm integral equations of the first as well as the second kind are studied. In addition to the solutions, the asymptotic behaviour of the eigenvalues for the basic equations of this type is also described. Many different techniques are presented to solve these integral equations. 1. Introdaction SINGULAR integral equations with logarithmic kernels arise in analysis and in many two-dimensional problems in mathematical physics, mechanics, and engineering