Total variation and cheeger sets in Gauss space

Caselles, Vicente; Miranda, Michele; Novaga, Matteo

doi:http://dx.doi.org/10.1016/j.jfa.2010.05.007

Total variation and cheeger sets in Gauss space

Citación

Caselles V, Miranda Jr. M, Novaga M. Total variation and cheeger sets in Gauss space. J Funct Anal. 2010 Sep 15;259(6):1491-516. DOI: 10.1016/j.jfa.2010.05.007

Resumen

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.