We give some a priori estimates of type sup*inf for Yamabe and prescribed
scalar curvature type equations on Riemannian manifolds of dimension >2. The
product sup*inf is caracteristic of those equations, like the usual Harnack
inequalities for non negative harmonic functions. First, we have a lower bound
for sup*inf for some classes of PDE on compact manifolds (like prescribed
scalar cuvature). We also have an upper bound for the same product but on any
Riemannian manifold not necessarily compact. An application of those result is
an uniqueness solution for some PDE.Comment: 16 page
