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Samy Skander Bahoura

Publications and source records attributed to Samy Skander Bahoura.

At least 37 records · Page 2Linked to original sources
arXiv2018

A uniform result in dimension 2

We give a uniqueness result in dimension 2 for the solutions to an equation on compact Riemannian surface without boundary.

math.DG↗
arXiv2018

An existence result

On compact Riemannian manifold of dimension n, and under some conditions on the curvature, we have changing-sign solutions for n large enough for an elliptic PDE.

math.AP↗
arXiv2014

On the mass of the exterior blow-up points

We consider the following problem on open set $Ω$ of ${\mathbb R}^2$: $$\left \{ \begin {split} -Δu_i & = V_i e^{u_i} \,\, &\text{in} \,\, &Ω\subset {\mathbb R}^2, \\ u_i & = 0 \,\, & \text{in} \,\, &\partial Ω.\end {split}\right.$$ We assume that $ \int_Ω e^{u_i} dy \leq C$, and $ 0 \leq V_i \leq b < + \infty$. On the other hand, if we assume that $V_i$ $s-$holderian with $1/2< s \leq 1$, then each exterior blow-up point is simple. As application, we have a compactness result for the case when: $\int_ΩV_i e^{u_i} dy \leq 40π-ε, \,\, ε>0$.

math.AP↗
arXiv2011

Uniqueness type result in dimension 3

We give some estimates of type sup*inf for equation of prescribed scalar curvature type in dimenion 3. As a consequence, we derive an uniqueness type result.

math.AP↗
arXiv2007

Lower bounds for sup + inf and sup * inf and an Extension of Chen-Lin result in dimension 3

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.

math.AP↗