Exterior convexity and classical calculus of variations

Abstract

We study the relation between various notions of exterior convexity introduced in Bandyopadhyay-Dacorogna-Sil \cite{BDS1} with the classical notions of rank one convexity, quasiconvexity and polyconvexity. To this end, we introduce a projection map, which generalizes the alternating projection for two-tensors in a new way and study the algebraic properties of this map. We conclude with a few simple consequences of this relation which yields new proofs for some of the results discussed in Bandyopadhyay-Dacorogna-Sil \cite{BDS1}.

The original publication is available at www.esaim-cocv.org https://www.esaim-cocv.org/articles/cocv/abs/2016/02/cocv150007/cocv150007.html

Cited by in corpus (2)

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