Image filtering, mean curvature, Dirichlet problems

Numerical experiments of the model for image filtering proposed in [1] by C randall, Lions and others show that, given the PDE, the differential proble m which is correct to solve is the Dirichlet one, on a domain Omega convex with holes. The aim of this paper is to produce a result of existence and u niqueness of the viscosity solution for this problem. The result is stated for convex domains and for nonconvex ones, we propose an easy example in or der to show that an existence theorem has not been expected. (C) 1999 Elsev ier Science Ltd. All rights reserved.