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. © 2009 Springer-Verlag.