arXiv:2004.10287 Abstract | arXiv Analytics

arXiv:2004.10287 [math.AP]Abstract References Reviews Resources

Hidden convexity in a problem of nonlinear elasticity

Nassif Ghoussoub, Young-Heon Kim, Hugo Lavenant, Aaron Zeff Palmer

Published 2020-04-21Version 1

We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of the pressure in the deformed configuration. We also provide a convex relaxation of the problem together with its dual formulation, based on measure-valued mappings, which coincides with the original problem under our condition.

Comments: 16 pages

Categories: math.AP, math.OC

Keywords: hidden convexity, incompressible nonlinear elasticity variational problems, global energy minimizer, dual formulation, convex relaxation

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