A variational principle for the equations of piezoelectromagnetism in elastic dielectric crystals

In a dielectric crystal of volume V bounded by a surface S which separates V from an outer vacuum V´, the kinetic energy density and the electric enthalpy density are defined. By introducing these density functions in a variational principle, and by requiring the independent variations of the mechanical displacement, and the scalar and vector potentials of the EM field, it is shown that the equations of piezoelectromagnetism and the appropriate jump conditions are obtained. This variational principle accommodates the derivation of the equations of piezoelectromagnetism and the appropriate boundary conditions. It includes the variational principles of the equations of elasticity, Maxwell´s equations, and the equations of piezoelectricity as special cases