| Issue |
ESAIM: COCV
Volume 22, Number 2, April-June 2016
|
|
|---|---|---|
| Page(s) | 338 - 354 | |
| DOI | https://doi.org/10.1051/cocv/2015007 | |
| Published online | 04 March 2016 | |
Exterior convexity and classical calculus of variations
1
Department of Mathematics & Statistics, IISER
Kolkata, Mohanpur - 741246, India
saugata.bandyopadhyay@iiserkol.ac.in
2
Section de Mathématiques, Station 8, EPFL,
1015
Lausanne,
Switzerland
swarnendu.sil@epfl.ch
Received:
20
July
2014
We study the relation between various notions of exterior convexity introduced in [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009–1039.] with the classical notions of rank one convexity, quasiconvexity and polyconvexity. To this end, we introduce a projection map, which generalizes the alternating projection for two-tensors in a new way and study the algebraic properties of this map. We conclude with a few simple consequences of this relation which yields new proofs for some of the results discussed in [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009–1039.].
Mathematics Subject Classification: 49-XX
Key words: Calculus of variations / rank one convexity / quasiconvexity / polyconvexity / exterior convexity / exterior form / differential form
© EDP Sciences, SMAI 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.