A compactness result for a Gelfand-Liouville system with Lipschitz condition

We give a quantization analysis to an elliptic system (Gelfand-Liouville type system) with Dirichlet condition. An application, we have a com-pactness result for an elliptic system with Lipschitz condition

sup+inf for Riemannian surfaces and sup*inf for for bounded domains of R^n, n>2

This paper is in relation with a Note of "Comptes Rendus de l'Academie des Sciences" 2005. We have an idea about a lower bounds of sup+inf (2 dimensions) and sup*inf (dimensions >2).Comment: 15 page

Harnack Inequalities for Yamabe Type Equations

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.Comment: 16 page