Calculus of Variations and Geometric Measure Theory

N. Ghoussoub - Y. H. Kim - H. Lavenant - A. Z. Palmer

Hidden convexity in a problem of nonlinear elasticity

created by lavenant on 21 Apr 2020
modified on 03 Nov 2020


Accepted Paper

Inserted: 21 apr 2020
Last Updated: 3 nov 2020

Journal: SIAM Journal on Mathematical Analysis
Year: 2020


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.