LOWER BOUNDS FOR SUP+INF AND SUP*INF AND AN EXTENSION OF CHEN-LIN RESULT IN DIMENSION 3

doi:10.1016/S0252-9602(08)60075-2

Abstract

Abstract:

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 (sup_K^u)^2s-1× inf

_Ωu ≤ c for positive solutions of △u=Vu⁵ on

Ω ∈R³ , where K is a compact set of Ω and V is s-Hölderian, s ∈]-1/2,1] . For the case s=1/2 and Ω= S₃, we prove that, if min_Ωu > m > 0 (for some particular constant m > 0), and the Hölderian 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.

Key words: sup×inf, sup + inf, Harnack inequality, moving-plane method

CLC Number:

35J60

Samy Skander Bahoura. LOWER BOUNDS FOR SUP+INF AND SUP*INF AND AN EXTENSION OF CHEN-LIN RESULT IN DIMENSION 3[J].Acta mathematica scientia,Series B, 2008, 28(4): 749-758.

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LOWER BOUNDS FOR SUP+INF AND SUP*INF AND AN EXTENSION OF CHEN-LIN RESULT IN DIMENSION 3

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