On uniqueness in the affine boundary value problem of the nonlinear elastic dielectric

Knops, Robin; Trimarco, Carmine

doi:10.2140/jomms.2006.1.925

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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

DOI: 10.2140/jomms.2006.1.925

Abstract

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.

Keywords

elastic dielectric, affine boundary values, uniqueness

Milestones

Received: 7 February 2006

Accepted: 21 April 2006

Published: 1 September 2006

Authors

R. J. Knops
School of Mathematics and Computer Sciences and the Maxwell Institute of Mathematical Sciences Heriot–Watt University Edinburgh EH14 Scotland United Kingdom

C. Trimarco
Dipartimento di Matematica Applicata Universitá di Pisa Via Buonarroti 1 I-56127 Pisa Italy

Vol. 1, No. 5, 2006

R. J. Knops and C. Trimarco

Abstract

Keywords

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Authors