  We prove regularity results for the unique minimizer of the total variation
functional, currently used in image processing analysis since the work by L.
Rudin, S. Osher and E. Fatemi. In particular we show that if the source term
$f$ 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 V. Caselles, A.
Chambolle and M. Novaga for dimension $N\leq 7$ and (in case of the global
regularity) for convex domains.
