De Donder-Weyl equations and multisymplectic geometry

Multisymplectic geometry is an adequate formalism to geometrically describe first order classical field theories. The De Donder-Weyl equations are treated in the framework of multisymplectic geometry, solutions are identified as integral manifolds of Hamiltonian multi-vector fields. In contrast to mechanics, solutions cannot be described by points in the multisymplectic phase space. Foliations of the configuration space by solutions and a multisymplectic version of Hamilton-Jacobi theory are also discussed.