Dirichlet and Neumann problems for Klein-Gordon-Maxwell systems
  This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet boundary conditions on the matter field, and either Dirichlet or Neumann boundary conditions on the electric potential. 
Pietro d'Avenia, Lorenzo Pisani, Gaetano Siciliano