We give two results about Harnack type inequalities. First, on Riemannian surfaces, we have an estimate of type sup + inf. The second result concern the solutions of prescribed scalar curvature equation on the unit ball of Rn with Dirichlet condition. Next, we give an inequality of type (supK u)2s-1 × influ ≤ c for positive solutions of Ωu = V u5 on Ω R3, where K is a compact set of Ω and V is s-Hlderian, s ∈] - 1/2, 1]. For the case s = 1/2 and Ω = S3, we prove that, if minΩ u > m > 0 (for some particular constant m > 0), and the H¨olderian constant A of V tends to 0 (in certain meaning), we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set of Ω.
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