  We discuss the relation between the canonical Hamilton-Jacobi theory and the
De Donder-Weyl Hamilton-Jacobi theory known in the calculus of variations using
the examples of a scalar field in curved space-time and general relativity. By
restricting ourselves to the Gaussian coordinates we show how the canonical
Hamilton-Jacobi equation of general relativity can be derived from the De
Donder-Weyl Hamilton-Jacobi formulation of the Einstein equations.
