The Initial Value Problem for Maxwell’s Equations for Two Media Separated by a Plane

Abstract

Let the column vectors

$$ E = \left( {\begin{array}{*{20}{c}} {{E_1}} \\ {{E_2}} \\ {{E_3}} \end{array}} \right),H = \left( {\begin{array}{*{20}{c}} {{H_1}} \\ {{H_2}} \\ {{H_3}} \end{array}} \right) $$

describe an electromagnetic field. Denoting the space coordinates by x ₁, x ₂, x ₃ and the time by t we put

$$ \xi i = \partial /\partial {{\mathbf{x}}_i},\tau = \partial /\partial t $$

This paper represents results obtained at the Institute of Mathematical Sciences, New York University, sponsored by the Office of Naval Research, United States Navy.