Acta mathematica scientia,Series B

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

Samy Skander Bahoura   

  1. Department of Mathematics, Patras University, 26500 Patras, Greece
  • Received:2006-11-01 Revised:2008-04-10 Online:2008-10-20 Published:2008-10-20
  • Contact: Samy Skander Bahoura

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

Ωuc 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

CLC Number: 

  • 35J60
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