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September/October 2015 Variational models for prestrained plates with Monge-Ampère constraint
Marta Lewicka, Pablo Ochoa, Mohammad Reza Pakzad
Differential Integral Equations 28(9/10): 861-898 (September/October 2015).

Abstract

We derive a new variational model in the description of prestrained elastic thin films. The model consists of minimizing a biharmonic energy of the out-of plane displacements $v\in W^{2,2}(\Omega, \mathbb{R})$, satisfying the Monge-Ampèere constraint: $$ \det\nabla^2v = f . $$ Here, $f=-\mbox{curl}^T\mbox{curl} (S_g)_{2\times 2}$ is the linearized Gauss curvature of the incompatibility (prestrain) family of Riemannian metrics $G^h= \mbox{Id}_3 + 2 h^\gamma S_g+ h.o.t.$, imposed on the referential configurations of the thin films with midplate $\Omega$ and small thickness $h$. We further discuss multiplicity properties of the minimizers of this model in some special cases.

Citation

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Marta Lewicka. Pablo Ochoa. Mohammad Reza Pakzad. "Variational models for prestrained plates with Monge-Ampère constraint." Differential Integral Equations 28 (9/10) 861 - 898, September/October 2015.

Information

Published: September/October 2015
First available in Project Euclid: 23 June 2015

zbMATH: 1363.74063
MathSciNet: MR3360723

Subjects:
Primary: 74B20, 74K20

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 9/10 • September/October 2015
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