Uniqueness of the nonlinear elastic dielectric affine boundary value problem on the whole space and on cone-like regions

Conservation laws derived from the energy–momentum tensor are employed to establish under suitable sufficient conditions uniqueness in affine boundary value problems for the homogeneous nonlinear elastic dielectric on the whole space and on certain cone-like regions. In particular, the electric enthalpy is assumed to be strictly quasi-convex for the whole space, and strictly rank-one convex for cone-like regions. Asymptotic behaviour is also stipulated. Uniqueness results for corresponding affine boundary value problems of homogeneous nonlinear elastostatics are a special case of those derived here.