I am struggling with a problem like this: In dimension $n\geq 3$, For the following uniformly elliptic equation, do we have interior gradient estimates? $$a^{ij}(x)u_{ij}(x)+u_{nn}=0.$$, where $i,j=1,\cdots, n-1.$ $\lambda id<(a^{ij})<\Lambda id$, namely the equation is uniformly elliptic. Is there any interior gradient estimates? More specifically, I need the estimate $|u_n|\leq C$ in the interior, where $C$ depends only on $|u|_{L^\infty}$ and the elliptic constant.