Regularity results for solutions of a class of Hamilton-Jacobi equations

The regularity of the gradient of viscosity solutions of first-order Hamilton-Jacobi equations partial derivative(t)u(t,x) + H(t, x, D(x)u(t,x)) = 0; t is an element of R+, x is an element of R-n, u(0,x)= u(0)(x), x is an element of R-n, is studied under a strict convexity assumption on H(t,x,). Estimates on the discontinuity set of Du are derived. Such estimates imply that solutions of the above problem are smooth in the complement of a closed H-n-rectifiable set. In particular, it follows that Du belongs to the class SBV, i.e., D(2)u is a measure with no Canter part.