We study integrals of the form , where , is continuous and is a -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.
Cite this article
Saugata Bandyopadhyay, Bernard Dacorogna, Swarnendu Sil, Calculus of variations with differential forms. J. Eur. Math. Soc. 17 (2015), no. 4, pp. 1009–1039DOI 10.4171/JEMS/525