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The geometric framework for the Hamilton-Jacobi theory developed in previousworks is extended for multisymplectic first-order classical field theories. TheHamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonianformalisms of these theories as a particular case of a more general problem,and the classical Hamilton-Jacobi equation for field theories is recovered fromthis geometrical setting. Particular and complete solutions to these problemsare defined and characterized in several equivalent ways in both formalisms,and the equivalence between them is proved. The use of distributions in jetbundles that represent the solutions to the field equations is the fundamentaltool in this formulation. Some examples are analyzed and, in particular, theHamilton-Jacobi equation for non-autonomous mechanical systems is obtained as aspecial case of our results.

Hamilton-Jacobi theory in multisymplectic classical field theories