[For the entire collection see Zbl 0722.00034).]
From the introduction: The integral equation (1) \(\pi^{-1}\int^ 1_{-1}[(y-x)^{-1} +y(y^ 2-x^ 2)/(y^ 2+x^ 2)]\allowbreak u(y)dy=f(x)\), \(-1<x<1\), subject to the condition (2) \(\int^ 1_{- 1}u(y)dy=0\) is considered. In equation (1) \(f\) is a given function, \(u\) is the unknown solution, and the first integral term is to be interpreted as a Cauchy principal value. The problem (1)-(2) arises in the study of a cruciform crack in an infinite isotropic elastic medium under constant load \(f\equiv 1\) along its four branches.
Results on the solvability and asymptotics of the solution are given and a numerical quadrature formula method for the solution of the integral equation is presented.