Construction of Green's Functions for the Two-dimensional Static Klein-Gordon Equation (Journal of Partial Differential Equations, 2011)
In contrast to the cognate Laplace equation, for which a vast number of Green's functions is available, the field is not that developed for the static Klein-Gordon equation. The latter represents, nonetheless, a natural area for application of some of the methods that are proven productive for the Laplace equation. The perspective looks especially attractive for the methods of images and eigenfunction expansion. This study is based on our experience recently gained on the construction of Green's functions for elliptic partial differential equations. An extensive list of boundary-value problems formulated for the static Klein-Gordon equation is considered. Computer-friendly representations of their Green's functions are obtained, most of which have never been published before.
Keywords: Static Klein-Gordon equation; Green's function