Some variational principles for discontinuous Maxwell's equations

In this paper, some variational principles are derived to directly calculate dielectric problems featuring a discontinuous surface. First, a two-field variational principle is deduced from Hamilton's principle for a regular dielectric region. Next, this variational principle is augmented through an involutory transformation, and then a twelve-field variational principle is formulated which generates, as its Euler-Lagrange equations, Maxwell's equations with discontinuous electromagnetic fields.