Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set
| dc.creator | Mora, Maria Giovanna | |
| dc.creator | Morini, Massimiliano | |
| dc.date | 2000-06-05 | |
| dc.date | 2001-05-03 | |
| dc.date.accessioned | 2026-07-07T04:35:43Z | |
| dc.date.available | 2026-07-07T04:35:43Z | |
| dc.description | Using a calibration method, we prove that, if w is a function which satisfies all Euler conditions for the Mumford-Shah functional on a two-dimensional domain, and the discontinuity set S of w is a regular curve connecting two boundary points, then there exists a uniform neighbourhood U of S such that w is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions. We show that Euler conditions do not guarantee in general the minimality of w in the class of functions with the same boundary value of w and whose extended graph is contained in a neighbourhood of the extended graph of w, and we give a sufficient condition in terms of the geometrical properties of the domain and the discontinuity set under which this kind of minimality holds. | |
| dc.description | 31 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0006032 | |
| dc.identifier | http://arxiv.org/abs/math/0006032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59350 | |
| dc.subject | Functional Analysis | |
| dc.title | Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set | |
| dc.type | text |