  Mobile charge in an electrolytic solution can in principle be represented as
the divergence of ionic polarization. After adding explicit solvent
polarization a finite volume of electrolyte can then be treated as a composite
non-uniform dielectric body. Writing the electrostatic interactions as an
integral over electric field energy density we show that the Poisson-Boltzmann
functional in this formulation is convex and can be used to derive the
equilibrium equations for electric potential and ion concentration by a
variational procedure developed by Ericksen for dielectric continua (Arch.
Rational Mech. Anal. 2007, 183, 299-313). The Maxwell field equations are
enforced by extending the set of variational parameters by a vector potential
representing the dielectric displacement which is fully transverse in a
dielectric system without embedded external charge. The electric field energy
density in this representation is a function of the vector potential and the
sum of ionic and solvent polarization making the mutual screening explicit.
