On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone
| dc.creator | Lemenant, Antoine | |
| dc.date | 2008-09-24 | |
| dc.date.accessioned | 2026-07-07T10:04:59Z | |
| dc.date.available | 2026-07-07T10:04:59Z | |
| dc.description | We show that if $(u,K)$ is a global minimizer for the Mumford-Shah functional in $R^N$, and if K is a smooth enough cone, then (modulo constants) u is a homogenous function of degree 1/2. We deduce some applications in $R^3$ as for instance that an angular sector cannot be the singular set of a global minimizer, that if $K$ is a half-plane then $u$ is the corresponding cracktip function of two variables, or that if K is a cone that meets $S^2$ with an union of $C^1$ curvilinear convex polygones, then it is a $P$, $Y$ or $T$. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/0809.4174 | |
| dc.identifier | http://arxiv.org/abs/0809.4174 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169878 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Spectral Theory | |
| dc.subject | 49Q20; 49Q05; 35J25; 35P15 | |
| dc.title | On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone | |
| dc.type | text |