A second order minimality condition for the Mumford-Shah functional
| dc.creator | Cagnetti, Filippo | |
| dc.creator | Mora, Maria Giovanna | |
| dc.creator | Morini, Massimiliano | |
| dc.date | 2007-04-24 | |
| dc.date.accessioned | 2026-07-07T07:57:56Z | |
| dc.date.available | 2026-07-07T07:57:56Z | |
| dc.description | A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(Γ)$, $Γ$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $Γ$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/0704.3124 | |
| dc.identifier | http://arxiv.org/abs/0704.3124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127832 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Optimization and Control | |
| dc.subject | 49K10; 49Q20 | |
| dc.title | A second order minimality condition for the Mumford-Shah functional | |
| dc.type | text |