In this paper we prove the special bounded variation regularity of the gradient of a viscosity solution of the Hamilton-Jacobi equation partial derivative(t)u + H(t, x, D(x)u) = 0 in Omega subset of [0, T] x R-n under the hypothesis of uniform convexity of the Hamiltonian H in the last variable. This result extends the result of Bianchini, De Lellis, and Robyr obtained for a Hamiltonian H = H(D(x)u) which depends only on the spatial gradient of the solution.
