Variational models for prestrained plates with Monge-Amp\`ere constraint
classification
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math-phmath.DGmath.MP
keywords
constraintmodelmonge-ampbiharmoniccasesconsistsdeformationsderive
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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-Amp\`ere constraint $\det\nabla^2v = f$. We further discuss multiplicity properties of the minimizers of this model, in some special cases.
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