  The geometric framework for the Hamilton-Jacobi theory developed in previous
works is extended for multisymplectic first-order classical field theories. The
Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian
formalisms of these theories as a particular case of a more general problem,
and the classical Hamilton-Jacobi equation for field theories is recovered from
this geometrical setting. Particular and complete solutions to these problems
are defined and characterized in several equivalent ways in both formalisms,
and the equivalence between them is proved. The use of distributions in jet
bundles that represent the solutions to the field equations is the fundamental
tool in this formulation. Some examples are analyzed and, in particular, the
Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a
special case of our results.
