  A previous knowledge of the domains of dependence of an Hamilton Jacobi
equation can be useful in its study and approximation. Information of this
nature are, in general, difficult to obtain directly from the data of the
problem. In this paper we introduce formally the concept of independent
sub-domains discussing their main properties and we provide a constructive
implicit representation formula. Using such results we propose an algorithm for
the approximation of these sets that will be shown to be relevant in parallel
computing of the solution.
