# Calculus of variations with differential forms

Saugata Bandyopadhyay; Bernard Dacorogna; Swarnendu Sil

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 4, page 1009-1039
- ISSN: 1435-9855

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topBandyopadhyay, Saugata, Dacorogna, Bernard, and Sil, Swarnendu. "Calculus of variations with differential forms." Journal of the European Mathematical Society 017.4 (2015): 1009-1039. <http://eudml.org/doc/277233>.

@article{Bandyopadhyay2015,

abstract = {We study integrals of the form $\int _\{\Omega \}f\left( d\omega \right)$, where $1\le k\le n$, $f:\Lambda ^\{k\}\rightarrow \mathbb \{R\}$ 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.},

author = {Bandyopadhyay, Saugata, Dacorogna, Bernard, Sil, Swarnendu},

journal = {Journal of the European Mathematical Society},

keywords = {calculus of variations; differential forms; quasiconvexity; polyconvexity and ext. one convexity; calculus of variations; differential forms; quasiconvexity; polyconvexity; ext. one convexity},

language = {eng},

number = {4},

pages = {1009-1039},

publisher = {European Mathematical Society Publishing House},

title = {Calculus of variations with differential forms},

url = {http://eudml.org/doc/277233},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Bandyopadhyay, Saugata

AU - Dacorogna, Bernard

AU - Sil, Swarnendu

TI - Calculus of variations with differential forms

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 4

SP - 1009

EP - 1039

AB - We study integrals of the form $\int _{\Omega }f\left( d\omega \right)$, where $1\le k\le n$, $f:\Lambda ^{k}\rightarrow \mathbb {R}$ 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.

LA - eng

KW - calculus of variations; differential forms; quasiconvexity; polyconvexity and ext. one convexity; calculus of variations; differential forms; quasiconvexity; polyconvexity; ext. one convexity

UR - http://eudml.org/doc/277233

ER -

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