2007/07/10 by Samy Skander Bahoura, Bahoura, Samy Skander
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.0707.1400
arxiv created 2007/07/10 · arxiv updated 2009/12/01
We give two results about Harnack type inequalities. First, on compact smooth Riemannian surface without boundary, we have an estimate of the type sup +inf. The second result concerns the solutions of prescribed scalar curvature equation on the unit ball of \mathbb Rn with Dirichlet condition. Next, we give an inequality of the type (supK u)2s-1 × infΩ u ≤ c for positive solutions of Δu=Vu5 on Ω⊂ \mathbb R3, where K is a compact set of Ω and V is s- hölderian, s∈ ]-1/2,1]. For the case s=1/2, we prove that if minΩ u>m>0 and the hölderian constant A of V is small enough (in certain meaning), we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set of Ω. ----- Nous donnons quelques estimations des solutions d'equations elliptiques sur les surfaces de Riemann et sur des ouverts en dimension n> 2. Nous traitons le cas holderien pour l'equation de la courbure scalaire prescrite en dimension 3.