In this paper we study the regularity of the solutions of viscosity solutions
of the following Hamilton-Jacobi equations
$$
\partial_t u + H(D_{x} u)=0 \qquad \textrm{in } \Omega\subset
\R\times \R^{n}\, .$$
In particular, under the assumption that the Hamiltonian
$H\in C^2(\R^n)$ is uniformly convex, we prove that the gradient $D_{x}u$
belongs to the class $SBV_{loc}(\Omega)$.
