Exact solutions of the multidimensional Lieu ville equation, which are soug
ht in the class of functional forms of the degree n equal to the coordinate
space dimension, are constructed based on a special representation of the
Laplace and D'Alembert equations. The corresponding Liouville equation solu
tions are completely described in the coordinate space dimensions d = 3,4.
For d > 4, the general solution form and the method for obtaining algebraic
equations for the coefficients of functional n-forms is presented.