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arXiv · 1712.00278

Exterior convexity and classical calculus of variations

Saugata Bandyopadhyay·Swarnendu Sil
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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}.

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Saugata Bandyopadhyay, Swarnendu Sil. 2017-12-01. Exterior convexity and classical calculus of variations. https://doi.org/10.1051/cocv%2F2015007

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