Geodesic
Exterior convexity and classical calculus of variations
Bandyopadhyay, Saugata1 ; Sil, Swarnendu2
1 Department of Mathematics & Statistics, IISER Kolkata, Mohanpur-741246, India
2 Section de Mathématiques, Station 8, EPFL, 1015 Lausanne, Switzerland
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 338-354

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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.].

Reçu le :
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, Tome 22 (2016) no. 2, pp. 338-354. doi: 10.1051/cocv/2015007

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