Harnack Inequalities for Yamabe Type Equations

Details Harnack Inequalities for Yamabe Type Equations Harnack Inequalities for Yamabe Type Equations

2006-04-25

arxiv.org/abs/math/0604529v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

We give some a priori estimates of type sup*inf for Yamabe and prescribed scalar curvature type equations on Riemannian manifolds of dimension >2. The product sup*inf is caracteristic of those equations, like the usual Harnack inequalities for non negative harmonic functions. First, we have a lower bound for sup*inf for some classes of PDE on compact manifolds (like prescribed scalar cuvature). We also have an upper bound for the same product but on any Riemannian manifold not necessarily compact. An application of those result is an uniqueness solution for some PDE.

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