Wellposedness of a nonlocal nonlinear diffusion equation of image processing
- Author(s): Guidotti, P
- Shao, Y
- et al.
Published Web Locationhttps://doi.org/10.1016/j.na.2016.11.003
© 2016 Elsevier Ltd Existence and uniqueness of solutions to non-smooth initial data are established for a slight modification of the degenerate regularization of the well-known Perona–Malik equation first proposed in Guidotti and Lambers (2009). The results heavily rely on the choice of an appropriate functional setting inspired by a recent approach to degenerate parabolic equations via so-called singular Riemannian manifolds (Amann, 2013, 2016).