Exterior convexity and classical calculus of variations
Department of Mathematics & Statistics, IISER
Kolkata, Mohanpur - 741246, India
2 Section de Mathématiques, Station 8, EPFL, 1015 Lausanne, Switzerland
We study the relation between various notions of exterior convexity introduced in [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009–1039.] 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 [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009–1039.].
Mathematics Subject Classification: 49-XX
Key words: Calculus of variations / rank one convexity / quasiconvexity / polyconvexity / exterior convexity / exterior form / differential form
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