Image filtering, mean curvature, Dirichlet problems Original Research Article

Numerical experiments of the model for image filtering proposed in [1] by Crandall, Lions and others show that, given the PDE, the differential problem which is correct to solve is the Dirichlet one, on a domain Ω convex with holes. The aim of this paper is to produce a result of existence and uniqueness of the viscosity solution for this problem. The result is stated for convex domains and for nonconvex ones, we propose an easy example in order to show that an existence theorem has not been expected.