Some properties of minimizers for the Chan-Esedoglu L1TV functional
| dc.creator | Vixie, Kevin R. | |
| dc.date | 2007-10-22 | |
| dc.date.accessioned | 2026-07-07T08:37:42Z | |
| dc.date.available | 2026-07-07T08:37:42Z | |
| dc.description | We present two results characterizing minimizers of the Chan-Esedoglu L1TV functional $F(u) \equiv \int |\nabla u | dx + λ\int |u - f| dx $; $u,f:\Bbb{R}^n \to \Bbb{R}$. If we restrict to $u = χ_Σ$ and $f = χ_Ω$, $Σ, Ω\in \Bbb{R}^n$, the $L^1$TV functional reduces to $E(Σ) = \Per(Σ) + λ|Σ\vartriangle Ω|$. We show that there is a minimizer $Σ$ such that its boundary $\partialΣ$ lies between the union of all balls of radius $\frac{n}λ$ contained in $Ω$ and the corresponding union of $\frac{n}λ$-balls in $Ω^c$. We also show that if a ball of radius $\frac{n}λ + ε$ is almost contained in $Ω$, a slightly smaller concentric ball can be added to $Σ$ to get another minimizer. Finally, we comment on recent results Allard has obtained on $L^1$TV minimizers and how these relate to our results. | |
| dc.identifier | https://arxiv.org/abs/0710.3980 | |
| dc.identifier | http://arxiv.org/abs/0710.3980 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140491 | |
| dc.subject | Optimization and Control | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Some properties of minimizers for the Chan-Esedoglu L1TV functional | |
| dc.type | text |