Vol. 1, No. 5, 2006

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ISSN: 1559-3959
On uniqueness in the affine boundary value problem of the nonlinear elastic dielectric

R. J. Knops and C. Trimarco

Vol. 1 (2006), No. 5, 925–936

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.

elastic dielectric, affine boundary values, uniqueness
Received: 7 February 2006
Accepted: 21 April 2006
Published: 1 September 2006
R. J. Knops
School of Mathematics and Computer Sciences and the Maxwell Institute of Mathematical Sciences
Heriot–Watt University
Edinburgh EH14
United Kingdom
C. Trimarco
Dipartimento di Matematica Applicata
Universitá di Pisa
Via Buonarroti 1
I-56127 Pisa