Variational models for prestrained plates with Monge-Ampère constraint

2014/04/12 by Marta Lewicka, Pablo Ochoa, Lewicka, Marta +3
Mathematics · Physics and Astronomy · #35Q74 #53A35 #74B20 #74K20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.DG #math.MP #msc:35Q74 #msc:53A35 #msc:74B20 #msc:74K20

paper · pdf · doi:10.48550/arxiv.1404.3298

27 pages

arxiv created 2014/04/12 · arxiv updated 2014/04/15

Abstract

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

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