Equilibria of charged hyperelastic solids

We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This involves the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in Eulerian coordinates. The ensuing electroelastic energy is then of mixed Lagrangian-Eulerian type. We prove that minimizers exist by investigating the continuity properties of the capacitary terms under convergence of the deformations.