Total variation and cheeger sets in Gauss space
The aim of this paper is to study the isoperimetric problem with fixed volume inside convex sets and other related geometric variational problems in the Gauss space, in both the finite and infinite dimensional case. We first study the finite dimensional case, proving the existence of a maximal Cheeg...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universitat Pompeu Fabra |
| Repositorio: | Repositorio Digital de la UPF |
| OAI Identifier: | oai:repositori.upf.edu:10230/36162 |
| Acceso en línea: | http://hdl.handle.net/10230/36162 http://dx.doi.org/10.1016/j.jfa.2010.05.007 |
| Access Level: | acceso abierto |
| Palabra clave: | Isoperimetric problems Wiener space Gaussian measures Cheeger sets |
| Sumario: | The aim of this paper is to study the isoperimetric problem with fixed volume inside convex sets and other related geometric variational problems in the Gauss space, in both the finite and infinite dimensional case. We first study the finite dimensional case, proving the existence of a maximal Cheeger set which is convex inside any bounded convex set. We also prove the uniqueness and convexity of solutions of the isoperimetric problem with fixed volume inside any convex set. Then we extend these results in the context of the abstract Wiener space, and for that we study the total variation denoising problem in this context. |
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