An integral identity is constructed from properties of the energy momentum tensor
and is used to demonstrate uniqueness of the displacement on star-shaped regions to
the affine boundary value problem of the nonlinear homogeneous elastic dielectric.
The method of proof, nontrivially adapted from that of the corresponding elastic
problem, assumes the electric enthalpy function to be rank-one convex and strictly
quasiconvex. Furthermore, for a given displacement gradient, the electric quantities
are proved unique for specified nonaffine and nonuniform electric boundary
conditions subject to the electric enthalpy and strain energy functions satisfying
additional convexity conditions.
School of Mathematics and Computer
Sciences and the Maxwell Institute of Mathematical
Sciences
Heriot–Watt University
Edinburgh EH14
Scotland
United Kingdom