Model nonlocal electrostatics. I

An approximate method for calculating the electrostatic potential due to external charges in systems with interfaces, involving components with spatially dispersive permittivities is developed. The method can be applied to systems with an arbitrary type of nonlocal dielectric response of the components and for a broad class of interfaces, separating the 'quasi-uniform' regions. All the solutions are obtained in the form of integrals from functions which are known and functions which can be determined from a Fredholm integral equation of the second kind. For a set of systems, its kernel provides an easy transformation of this equation to a simple differential one, so that the solutions are obtained in an analytical form. As an example, the contact of two media at a plane interface is considered.