Calculus of variations with differential forms

Bandyopadhyay, 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 -