Calculus of variations with differential forms
Saugata Bandyopadhyay, Bernard Dacorogna, Swarnendu Sil · Journal of the European Mathematical Society · 2015
We study integrals of the form \int_{\Omega}f\left( d\omega\right) , where 1\leq k\leq n , f:\Lambda^{k}\rightarrow\mathbb{R} is continuous and \omega is a \left(k-1\right) -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.