On the regularity of the total variation minimizers
Alessio Porretta · Communications in Contemporary Mathematics · 2019
We prove regularity results for the unique minimizer of the total variation functional, currently used in image processing analysis since the work by Rudin, Osher and Fatemi. In particular, we show that if the source term [Formula: see text] is locally (respectively, globally) Lipschitz, then the solution has the same regularity with local (respectively, global) Lipschitz norm estimated accordingly. The result is proved in any dimension and for any (regular) domain. So far we extend a similar result proved earlier by Caselles, Chambolle and Novaga for dimension [Formula: see text] and (in case of the global regularity) for convex domains.