ABSTRACT
The location of singularities of solutions to elliptic differential equations has frequently an important application. In the case of fluid flows the singularities correspond to either sinks or sorces which suggests they might be used for various purposes. For example Cohen and Gilbert [Cogi57] used a method of images to set up an integral equation for the line source density supporting the cavitation flow around a thin projectile in a channel. Fundamental singularities are useful for setting up boundary integral methods; see in this respect the discussion of the single layer method developed by Fichera [Fich61] discussed in Chapter II, and the literature cited at the end of that chapter. The technique for developing a series expansion of the Bergman reproducing kernel made use of a geometric entity which involved the integral of a fundamental singularity. The nature and location of singularities has also played a big role in modern quantum scattering theory. In potential scattering one was concerned with the location of the Regge poles [Newt66], [Alre65], [Gilb69b]. In quantum field theory, according to the Mandelstam hypothesis the scattering amplitude could be expressed as a holomorphic function of three complex variables. The location of singularities of this function kept mathematicians and physicists occupied for some time [Gilb69b].
