Wellposedness of a nonlocal nonlinear diffusion equation of image processing

摘要

Existence and uniqueness are established for a degenerate regularization ofthe well-known Perona-Malik equation proposed by the first author fornon-smooth initial data. The results heavily rely on the choice of appropriatefunctional setting inspired by a recent approach to degenerate parabolicequations via so-called singular Riemannian manifolds introduced by HerbertAmann.