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Open Access Publications from the University of California

Wellposedness of a nonlocal nonlinear diffusion equation of image processing

  • Author(s): Guidotti, P
  • Shao, Y
  • et al.

© 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).

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