Regularity results for eikonal-type equations with nonsmooth coefficients

Solutions of the Hamilton-Jacobi equation H(x,-Du(x)) = 1, where H(center dot, p) is Holder continuous and the level-sets {H(x, center dot) a parts per thousand currency sign 1} are convex and satisfy positive lower and upper curvature bounds, are shown to be locally semiconcave with a power-like modulus. An essential step of the proof is the -regularity of the extremal trajectories associated with the multifunction generated by D (p) H