Propagation of singularities for solutions of nonlinear first order partial differential equations

Few results are available in the mathematical literature for studying the structure of the singular set of a weak solution u of F (x, u, Du) = 0. This paper provides new techniques to analyse such a set when u is semiconcave and F is a nonlinear convex function with respect to p. The main objective achieved here is a classification of the singularities of u that propagate along Lipschitz arcs. Such a propagation phenomenon is also described by means of a generalized characteristics inclusion.