Wellposedness of a nonlocal nonlinear diffusion equation of image   processing
  Existence and uniqueness are established for a degenerate regularization of the well-known Perona-Malik equation proposed by the first author for non-smooth initial data. The results heavily rely on the choice of appropriate functional setting inspired by a recent approach to degenerate parabolic equations via so-called singular Riemannian manifolds introduced by Herbert Amann. 
Patrick Guidotti, Yuanzhen Shao
math.AP