摘要：
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.
中图分类号:
Samy Skander Bahoura. LOWER BOUNDS FOR SUP+INF AND SUP*INF AND AN EXTENSION OF CHEN-LIN RESULT IN DIMENSION 3[J]. 数学物理学报(英文版), 2008, 28(4): 749-758.
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.