On multiwell Liouville theorems in higher dimension
| dc.creator | Jerrard, Robert L. | |
| dc.creator | Lorent, Andrew | |
| dc.date | 2008-02-06 | |
| dc.date.accessioned | 2026-07-07T09:19:05Z | |
| dc.date.available | 2026-07-07T09:19:05Z | |
| dc.description | We consider certain subsets of the space of $n\times n$ matrices of the form $K = \cup_{i=1}^m SO(n)A_i$, and we prove that for $p>1, q \geq 1$ and for connected $Ω'\subset\subsetΩ\subset \R^n$, there exists positive constant $a<1$ depending on $n,p,q, Ω, Ω'$ such that for $ \veps=\| {dist}(Du, K)\|_{L^p(Ω)}^p$ we have $\inf_{R\in K}\|Du-R\|^p_{L^p(Ω')}\leq M\veps^{1/p}$ provided $u$ satisfies the inequality $\| D^2 u\|_{L^q(Ω)}^q\leq a\veps^{1-q}$. Our main result holds whenever $m=2$, and also for {\em generic} $m\le n$ in every dimension $n\ge 3$, as long as the wells $SO(n)A_1,..., SO(n)A_m$ satisfy a certain connectivity condition. These conclusions are mostly known when $n=2$, and they are new for $n\ge 3$. | |
| dc.description | 35 pages | |
| dc.identifier | https://arxiv.org/abs/0802.0850 | |
| dc.identifier | http://arxiv.org/abs/0802.0850 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154259 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 26B99, 30C70 | |
| dc.title | On multiwell Liouville theorems in higher dimension | |
| dc.type | text |