The Dirichlet problem in a heterogeneous dielectric

摘要

A Green’s function has been used to discuss the Dirichlet problem in a heterogeneous dielectric. Depending on the boundary condition imposed on the Green’s function, one obtains formal expressions for the potential and the electric field or bounds on the potential and the field components at a point. A formal expression for the effective permittivity of a random statistically homogeneous dielectric has also been obtained. Finally, the Green’s function has been obtained in terms of a Neumann series. A close relation is observed between the Green’s function and the T matrix used in treating effective constants.