Calculus of Variations and Partial Differential Equations

, Volume 26, Issue 2, pp 171–199

Existence of infinitely many solutions for the one-dimensional Perona-Malik model

Original Article

DOI: 10.1007/s00526-005-0363-4

Cite this article as:
Zhang, K. Calc. Var. (2006) 26: 171. doi:10.1007/s00526-005-0363-4

Abstract

We establish the existence of infinitely many weak solutions for the the one-dimensional version of the well-known and widely used Perona-Malik anisotropic diffusion equation model in image processing. We establish the existence result under the homogeneous Neumann condition with smooth non-constant initial values. Our method is to convert the problem into a partial differential inclusion problem.

Keywords

Perona-Malik modelOne-dimensionalInfinitely many solutionsDifferential inclusionRelaxation property

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SussexBrightonUK