  We perform a non-perturbative analysis of the constraints of the Ho\v{r}ava
Gravitational theory. In distinction to Einstein gravity the theory has
constraints of the first class together with second class ones. We analyze the
consequences of having to impose second classes constraints at any time in the
quantum formulation of the theory. The second class constraints are formulated
as strongly elliptic partial differential equations allowing a global analysis
on the existence and uniqueness of the solution. We discuss the possibility of
formulating the theory in terms of a master action with first class constraints
only. In this case the Ho\v{r}ava theory would correspond to a gauged fixed
version of the master theory. Finally we obtain, using the non-perturbative
solution of the constraints, the explicit expression of the gravitational
energy. It is, under some assumptions, always positive and the solution of
Ho\v{r}ava field equations at minimal energy is the Minkowski metric.
