Acta mathematica scientia, Series B >

2008 , Vol. 28 >Issue 4: 749 - 758

DOI: https://doi.org/10.1016/S0252-9602(08)60075-2

Articles

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

  • Samy Skander Bahoura
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  • Department of Mathematics, Patras University, 26500 Patras, Greece

Received date: 2006-11-01

  Revised date: 2008-04-10

  Online published: 2008-10-20

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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 (supKu)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 minΩu > 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

Cite this article

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 . DOI: 10.1016/S0252-9602(08)60075-2

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