Some Uniforme Estimates for Scalar Curvature Type Equations

We consider the prescribed scalar curvature equation on an open setΩ of Rn,∆u = V u(n+2)/(n−2) + un/(n−2) with V ∈ C1,α (0 < α ≤ 1) and we prove the inequality supK u× infΩ u ≤ c where K is a compact set of Ω. In dimension 4, we have an idea on the supremum of the solution of the prescribed scalar curvature if we control the infimum. For this case we suppose the scalar curvature C1,α, (0 < α ≤ 1).