Variational models for prestrained plates with Monge-Ampère constraint

Abstract

We derive a new model for pre-strained thin films, which consists of minimizing a biharmonic energy of deformations $v\in W^{2,2}$ satisfying the Monge-Ampère constraint $\det {\nabla }^{2}v=f$. We further discuss multiplicity properties of the minimizers of this model, in some special cases.

27 pages

References in corpus (2)

• Elastic theory of unconstrained non-Euclidean plates
• Plates with incompatible prestrain of higher order

Cited by in corpus (2)

• Plates with incompatible prestrain of higher order
• The linearized Kirchhoff theory for plates with incompatible prestrain