Vol. 1, No. 5, 2006

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 4, 541–572
Issue 3, 303–540
Issue 2, 157–302
Issue 1, 1–156

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 1559-3959
ISSN (print): 1559-3959
Author index
To appear
Other MSP journals
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