Lower bounds for sup + inf and sup * inf and an Extension of Chen-Lin result in dimension 3
| dc.creator | Bahoura, Samy Skander | |
| dc.date | 2007-07-10 | |
| dc.date.accessioned | 2026-07-07T08:14:50Z | |
| dc.date.available | 2026-07-07T08:14:50Z | |
| dc.description | We give two results about Harnack type inequalities. First, on compact smooth Riemannian surface without boundary, we have an estimate of the type $\sup +\inf$. The second result concerns the solutions of prescribed scalar curvature equation on the unit ball of ${\mathbb R}^n$ with Dirichlet condition. Next, we give an inequality of the type $(\sup_K u)^{2s-1} \times \inf_Ω u \leq c$ for positive solutions of $Δu=Vu^5$ on $Ω\subset {\mathbb R}^3$, where $K$ is a compact set of $Ω$ and $V$ is $s-$ hölderian, $s\in ]-1/2,1]$. For the case $s=1/2$, we prove that if $\min_Ω u>m>0$ and the hölderian constant $A$ of $V$ is small enough (in certain meaning), we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set of $Ω$. ----- Nous donnons quelques estimations des solutions d'equations elliptiques sur les surfaces de Riemann et sur des ouverts en dimension n> 2. Nous traitons le cas holderien pour l'equation de la courbure scalaire prescrite en dimension 3. | |
| dc.identifier | https://arxiv.org/abs/0707.1400 | |
| dc.identifier | http://arxiv.org/abs/0707.1400 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133269 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Lower bounds for sup + inf and sup * inf and an Extension of Chen-Lin result in dimension 3 | |
| dc.type | text |