Regularity results for eikonal-type equations with nonsmooth coefficients

Abstract

Solutions of the Hamilton-Jacobi equation H(x,-Du(x)) = 1, where H(·, p) is Hölder continuous and the level-sets {H(x, ·) ≤ 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 C 1,α-regularity of the extremal trajectories associated with the multifunction generated by D pH. © 2012 Springer Basel AG.