Calculus of Variations and Geometric Measure Theory
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V. Caselles - M. Miranda Jr - M. Novaga

Total Variation and Cheeger Sets in Gauss Space

created by miranda on 19 Oct 2009
modified on 16 Nov 2012


Published Paper

Inserted: 19 oct 2009
Last Updated: 16 nov 2012

Journal: J. Funct. Anal.
Volume: 259
Number: 6
Pages: 1491-1516
Year: 2010
Doi: 10.1016/j.jfa.2010.05.007


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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