Exterior convexity and classical calculus of variations
ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 2, pp. 338-354.

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.].

Received:
DOI: 10.1051/cocv/2015007
Classification: 49-XX
Keywords: Calculus of variations, rank one convexity, quasiconvexity, polyconvexity, exterior convexity, exterior form, differential form
Bandyopadhyay, Saugata 1; Sil, Swarnendu 2

1 Department of Mathematics & Statistics, IISER Kolkata, Mohanpur-741246, India
2 Section de Mathématiques, Station 8, EPFL, 1015 Lausanne, Switzerland
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Bandyopadhyay, Saugata; Sil, Swarnendu. Exterior convexity and classical calculus of variations. ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 2, pp. 338-354. doi : 10.1051/cocv/2015007. http://archive.numdam.org/articles/10.1051/cocv/2015007/

S. Bandyopadhyay, B. Dacorogna and S. Sil, Calculus of variations with differential forms, J. Eur. Math. Soc. 17 (2015) 1009–1039. | DOI | MR | Zbl

S. Bandyopadhyay and S. Sil, Characterization of functions affine in the direction of one-divisible forms. In preparation.

B. Dacorogna, Direct methods in the calculus of variations. In vol. 78 of Appl. Math. Sci. 2nd edition. Springer, New York (2008). | MR | Zbl

S. Sil, Ph.D. thesis.

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