General solution of a 2-D weak singular integral equation with constraint and its applications (Q1387560)

The paper is concerned with the integral equation \[ \int_{0}^{\pi} \int_{-\infty}^{\infty} k(\psi)p(s,\psi)ds d\psi = F(r,\theta), \quad (r,\theta)\in Q , \] subject to the constraints \[ p(s,\psi)=0, \quad (s,\psi)=(r,\theta)\notin Q= \{(r,\theta):F(r,\theta)>c_0 \}, \] which occurs in computerized tomography, electric chemistry and contact problems. Here \(k\) and \(F\) are given continuous functions, \((r,\theta)\) are the polar coordinates centred at the origin, and \((s,\psi)\) are local polar coordinates. The solution of (1) is obtained from the reduced standard Abel integral equation by applying the Radon transform. As an example, the solution of the contact problem between a rigid cone and an elastic half--space is given.