JournalsjemsVol. 17, No. 4pp. 1009–1039

Calculus of variations with differential forms

  • Saugata Bandyopadhyay

    IISER Kolkata, Mohanpur, India
  • Bernard Dacorogna

    Ecole Polytechnique Fédérale de Lausanne, Switzerland
  • Swarnendu Sil

    Ecole Polytechnique Fédérale de Lausanne, Switzerland
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Abstract

We study integrals of the form Ωf(dω)\int_{\Omega}f\left( d\omega\right), where 1kn1\leq k\leq n, f:ΛkRf:\Lambda^{k}\rightarrow\mathbb{R} is continuous and ω\omega is a (k1)\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.

Cite this article

Saugata Bandyopadhyay, Bernard Dacorogna, Swarnendu Sil, Calculus of variations with differential forms. J. Eur. Math. Soc. 17 (2015), no. 4, pp. 1009–1039

DOI 10.4171/JEMS/525