Complex Variable Hypersingular Integral Equations (CVH-BIE)

Abstract

As noted in chapter 10, hypersingular integrals can be obtained by differentiation of singular integrals and/or integration by parts. This gives a connection between complex variable hypersingular and singular equations. Hence, we can construct a theory of complex variable hypersingular equations (CVH-BIE) by employing the well-established theory of singular integral equations (SIE). We use such an approach in the theoretical discussion in this chapter. Paragraphs 49–51 reproduce the results briefly presented in papers by Linkov and Mogilevskaya (Linkov and Mogilevskaya [4], Linkov, Zoubkov and Mogilevskaya [1]). The general case of the plane elasticity problem for a set of open and closed contours is presented in § 52 for the first time.