A method for reduction of differential problems to integral equations

A differential problem in an arbitrary domain is replaced with a problem with the same differential operator posed in a canonical domain for which the solution is either easily written out or is relatively easy to construct in terms of a function which is already known on the boundary of the canonical domain. The function is determined using the boundary conditions of the original problem, which in general leads to an integral equation. Some typical problems of mathematical physics are considered as an example.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 62, pp. 8–14, 1987.