On some nonlinear partial differential equations involving the 1-Laplacian
| dc.creator | Kraiem, Mouna | |
| dc.date | 2007-03-16 | |
| dc.date.accessioned | 2026-07-07T07:52:22Z | |
| dc.date.available | 2026-07-07T07:52:22Z | |
| dc.description | In this paper we present an approximation result concerning the first eigenvalue of the 1-Laplacian operator. More precisely, for $Ω$ a bounded regular open domain, we consider a minimisation of the functional ${\ds \int_Ω}|\nabla u|+n({\ds \int_Ω} |u|-1)^2 $ over the space $W_0^{1,1}(Ω)$. For $n$ large enough, the infimum is achieved in some sense on $BV(Ω)$, and letting $n$ go to infinity this provides an approximation of the first eigenfunction for the first eigenvalue, since the term $n({\ds \int_Ω} |u|^2-1)^2$ "tends" to the constraint $\|u\|_1=1$. | |
| dc.description | 16pages | |
| dc.identifier | https://arxiv.org/abs/math/0703497 | |
| dc.identifier | http://arxiv.org/abs/math/0703497 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125853 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J70, 35J60 | |
| dc.title | On some nonlinear partial differential equations involving the 1-Laplacian | |
| dc.type | text |