an:04160048
Zbl 0706.65114
Golovach, G. P.
A method for the reduction of differential problems to integral equations
RU
Vychisl. Prikl. Mat., Kiev 62, 8-14 (1987).
00224242
1987
j
65N35 65R20 35J05 35C15 45E10
Laplace equation; integral equation method; canonical region
Summary: Given a differential problem in an arbitrary region. It is suggested to solve a different problem instead with the same differential operator but in a canonical region. Its solution can be written down easily or at least simply be formulated in terms of a function that is unknown on the surface of the canonical region. Boundary conditions of the initial problem are exploited to derive this unknown function and this results in an integral equation. Several typical problems of mathematical physics serve as an example.