A Polyconvex Integrand; Euler-Lagrange Equations and Uniqueness of Equilibrium

Roméo Awi, Wilfrid Gangbo

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this manuscript we are interested in stored energy functionals W defined on the set of d × d matrices, which not only fail to be convex but satisfy (Formula presemted.). We initiate a study which we hope will lead to a theory for the existence and uniqueness of minimizers of functionals of the form (Formula presented.), as well as their Euler-Lagrange equations. The techniques developed here can be applied to a class of functionals larger than those considered in this manuscript, although we keep our focus on polyconvex stored energy functionals of the form (Formula presented.) - such that (Formula presented.) - which appear in the study of Ogden material. We present a collection of perturbed and relaxed problems for which we prove uniqueness results. Then, we characterize these minimizers by their Euler-Lagrange equations.

Original languageEnglish (US)
Pages (from-to)143-182
Number of pages40
JournalArchive For Rational Mechanics And Analysis
Volume214
Issue number1
DOIs
StatePublished - Oct 2014

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