  A new approach leading to the formulation of the Hamilton-Jacobi equation for
field theories is investigated within the framework of jet-bundles and
multi-symplectic manifolds. An algorithm associating classes of solutions to
given sets of boundary conditions of the field equations is provided. The paper
also puts into evidence the intrinsic limits of the Hamilton-Jacobi method as
an algorithm to determine families of solutions of the field equations, showing
how the choice of the boundary data is often limited by compatibility
conditions.
