A lower semicontinuity result for some integral functionals in the space SBD
| dc.creator | Ebobisse, Francois | |
| dc.date | 2003-06-30 | |
| dc.date.accessioned | 2026-07-07T04:59:17Z | |
| dc.date.available | 2026-07-07T04:59:17Z | |
| dc.description | The purpose of this paper is to study the lower semicontinuity with respect to the strong $L^1$-convergence, of some integral functionals defined in the space SBD of special functions with bounded deformation. Precisely, let $U$ be a bounded open subset of $R^n$. If $u\in $SBD$(U)$, $(u_h)\subset $SBD$(U)$ converges to $u$ strongly in $L^1(U,R^n)$ and the measures $|E^ju_h|$ converge weakly * to a measure $ν$ singular with respect to the Lebesgue measure, then $$\int_Uf(x,{\mathcal E}u)dx\leq\liminf_{h\to\infty} \int_Uf(x,{\mathcal E}u_h)dx$$ provided $f$ satisfies some weak convexity property and the standard growth assumptions of order $p>1$. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0306428 | |
| dc.identifier | http://arxiv.org/abs/math/0306428 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67925 | |
| dc.subject | Functional Analysis | |
| dc.subject | 49J45; 49Q20; 74C15 | |
| dc.title | A lower semicontinuity result for some integral functionals in the space SBD | |
| dc.type | text |