Hyperbolic potential theory in two dimensions

Summary

In this paper we show that the classical approach through “single” and “double” layer potentials based on the fundamental solution as a kernel leads in a natural way to simple solutions of the boundary value problems for hyperbolic equations in two independent variables. The “hyperbolic potentials” defined here are closely analogous to the thermal potentials as well as to the potentials arising in the study of elliptic equations. This extension of the use of potentials for studying boundary value problems for hyperbolic equations thus establishes the idea of potential as one of the unifying concepts of partial differential equations: it is now applicable to all three types of second order equations.