Propagation of graphs in two-dimensional inhomogeneous media

We consider the propagation of a front in a two-dimensional striated medium. In the case of a front that can be written as a graph over the real line we are led to an Eikonal equation for the height function which contains a possibly discontinuous coefficient. We prove existence and uniqueness of a viscosity solution in the sense of Ishii. Furthermore, we obtain an -error bound for a monotone and consistent finite difference scheme. We conclude with some numerical tests.