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math.AP2013
Higher-dimensional solutions for a nonuniformly elliptic equation
Mostafa Fazly
We prove -dimensional symmetry results, that we call -Liouville theorems, for stable and monotone solutions of the following nonuniformly elliptic equation \begin{eqnarray*}\…
math.AP2013
A pointwise inequality for the fourth order Lane-Emden equation
Mostafa Fazly, Juncheng Wei, Xingwang Xu
We prove that the following pointwise inequality holds \begin{equation*} -Δu \ge \sqrt\frac{2}{(p+1)-c_n} |x|^{\frac{a}{2}} u^{\frac{p+1}{2}} + \frac{2}{n-4} \frac{|\nabla u|^2}{u}…
math.AP2013
Liouville theorems for the polyharmonic Henon-Lane-Emden system
Mostafa Fazly
We study Liouville theorems for the following polyharmonic Hénon-Lane-Emden system \begin{eqnarray*} \left\{\begin{array}{lcl} (-Δ)^m u&=& |x|^{a}v^p \ \ \text{in}\ \ \mathbb{R}^n,…