Hidden convexity in a problem of nonlinear elasticity
Analysis of PDEs
2020-11-04 v2 Optimization and Control
Abstract
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.
Cite
@article{arxiv.2004.10287,
title = {Hidden convexity in a problem of nonlinear elasticity},
author = {Nassif Ghoussoub and Young-Heon Kim and Hugo Lavenant and Aaron Zeff Palmer},
journal= {arXiv preprint arXiv:2004.10287},
year = {2020}
}
Comments
17 pages