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}…