D. V. Kovkov ,   V. I. Tsurkov Journal of Computer and Systems Sciences International , Vol.39 No.4 , 01.2000 , p. 497-502, language: английский ISSN 1064-2307  Аннотация For the equations of anisotropic diffusion that are used in image processing, a class of functions of the existence of the weak solution to the Cauchy problem in the form of Holder-continuous functions is found. The results of the numerical computations show that infinite gradients (edges) are protected simultaneously with noise elimination.  Ключевые слова anisotropic diffusion, singularities, weak solutions, Holder-continuous functions