On the relationship between rank-$(n-1)$ convexity and ${\mathcal S}$-quasiconvexity
| dc.creator | Palombaro, Mariapia | |
| dc.date | 2009-04-27 | |
| dc.date.accessioned | 2026-07-07T13:08:59Z | |
| dc.date.available | 2026-07-07T13:08:59Z | |
| dc.description | We prove that rank-$(n-1)$ convexity does not imply ${\mathcal S}$-quasiconvexity (i.e., quasiconvexity with respect to divergence free fields) in ${\mathbb M}^{m\times n}$ for $m>n$, by adapting the well-known Sverak's counterexample [5] to the solenoidal setting. On the other hand, we also remark that rank-$(n-1)$ convexity and ${\mathcal S}$-quasiconvexity turn out to be equivalent in the space of $n\times n$ diagonal matrices. This follows by a generalization of Mueller's work [4]. | |
| dc.identifier | https://arxiv.org/abs/0904.4190 | |
| dc.identifier | http://arxiv.org/abs/0904.4190 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228599 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 49J45 | |
| dc.title | On the relationship between rank-$(n-1)$ convexity and ${\mathcal S}$-quasiconvexity | |
| dc.type | text |