Energy improvement for energy minimizing functions in the complement of generalized Reifenberg-flat sets
| dc.creator | Lemenant, Antoine | |
| dc.date | 2008-06-18 | |
| dc.date.accessioned | 2026-07-07T09:45:21Z | |
| dc.date.available | 2026-07-07T09:45:21Z | |
| dc.description | Let P be an hyperplane in R^N, and denote by dH the Hausdorff distance. We show that for all positive radius r < 1 there is an epsilon > 0, such that if K is a Reifenberg-flat set in B(0; 1), a ball in R^N, that contains the origin, with d_H(K; P) <epsilon, and if u is an energy minimizing function in B(0; 1)\K with restricted values on @B(0; 1)\K, then the normalized energy of u in B(0; r)\K is bounded by the normalized energy of u in B(0; 1)\K. We also prove the same result in R^3 when K is a epsilon-minimal set, that is a generalization of Reifenberg-flat sets with minimal cones of type Y and T. Moreover, the result is still true for a further generalization of sets called (eps; eps_0)-minimal. This article is a preliminary study for a forthcoming paper where a regularity result for the singular set of the Mumford-Shah functional close to minimal cones in R^3 is proved by the same author. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/0806.2987 | |
| dc.identifier | http://arxiv.org/abs/0806.2987 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163167 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 49Q20 | |
| dc.title | Energy improvement for energy minimizing functions in the complement of generalized Reifenberg-flat sets | |
| dc.type | text |