## Exterior Convexity And Classical Calculus Of Variations

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.].

Published in:
Esaim-Control Optimisation And Calculus Of Variations, 22, 2, 338-354
Year:
2016
Publisher:
Les Ulis Cedex A, Edp Sciences S A
ISSN:
1292-8119
Keywords:
Laboratories: