Exterior convexity and classical calculus of variations
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...
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| Published in | ESAIM. Control, optimisation and calculus of variations Vol. 22; no. 2; pp. 338 - 354 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Les Ulis
EDP Sciences
01.04.2016
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1292-8119 1262-3377 |
| DOI | 10.1051/cocv/2015007 |
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| Abstract | 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.]. |
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| AbstractList | We study the relation between various notions of exterior convexity introduced in Bandyopadhyay-Dacorogna-Sil [1] 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 Bandyopadhyay-Dacorogna-Sil [1]. 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.]. |
| Author | Sil, Swarnendu Bandyopadhyay, Saugata |
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| Keywords | differential form exterior form calculus of variations vexity polycon quasiconvexity exterior convexity 2010 Mathematics Subject Classification: 49-XX rank one convexity |
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| SubjectTerms | 49-XX Calculus of variations Convexity differential form exterior convexity exterior form Functional Analysis Mathematical analysis Mathematics polyconvexity quasiconvexity rank one convexity Tensors |
| Title | Exterior convexity and classical calculus of variations |
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