Wellposedness of a nonlocal nonlinear diffusion equation of image processing

Abstract

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.

References in corpus (4)

• Anisotropic Function Spaces on Singular Manifolds
• Singular parabolic equations of second order on manifolds with singularities
• The Yamabe flow on incomplete manifolds
• A Class Of Elliptic Equations with Interior Degeneration

Cited by in corpus (3)

• A Class Of Elliptic Equations with Interior Degeneration
• Degenerate parabolic $p$-Laplacian equations: existence, uniqueness and asymptotic behavior of solutions
• Maximal $L_q$-regularity of nonlocal parabolic equations in higher order Bessel potential spaces