Discontinuous solutions for Hamilton-Jacobi equations: Uniqueness and regularity

The uniqueness of classical semicontinuous viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations with convex Hamiltonians H = H (Du) is established, provided the discontinuous initial value function φ(x) is continuous outside a set Γ of measure zero and satisfies φ(x) ≥ φ**(x) ≡ li...