Geodesic
Calculus of variations with differential forms
Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 1009-1039.

Voir la notice de l'article provenant de la source EMS Press

We study integrals of the form ∫Ω​f(dω), where 1≤k≤n, f:Λk→R is continuous and ω is a (k−1)-form. We introduce the appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity. We study their relations, give several examples and counterexamples. We finally conclude with an application to a minimization problem.
DOI : 10.4171/jems/525
Classification : 49-XX
Keywords: Calculus of variations, differential forms, quasiconvexity, polyconvexity and ext. one convexity 
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     title = {Calculus of variations with differential forms},
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Saugata Bandyopadhyay; Bernard Dacorogna; Swarnendu Sil. Calculus of variations with differential forms. Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 1009-1039. doi : 10.4171/jems/525. http://geodesic.mathdoc.fr/articles/10.4171/jems/525/

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