SOME GLOBAL FEATURES OF WAVE PROPAGATION

After a discussion on two fundamental routes —weak discontinuity waves and high frequency asymptotic waves— both leading to Hamilton-Jacobi equation, we review two notions of weak solution for it, the minimax solution and the viscosity so- lution. We claim the coincidence of the two solutions for a general class of p-convex Hamiltonians of mechanical type and we sketch some technical details of the proof.