Hypersingular integral equation

Summary

A hypersingular integral equation is an integral equation with a very singular kernel. Its integral exists neither as an ordinary integral nor as a Cauchy principal value. The typical kernel on an interval is $1/(t - x)^2$, and the integral is read as a Hadamard finite part. Such equations arise in crack problems of elasticity and in the scattering of waves by thin screens. They also arise in boundary element methods that use the normal derivative of a double layer potential.