# ap.analysis of pdes – About the proof of higher regularity boundary Harnack inequality

I’m reading a note on higher regularity boundary Harnack inequality by D. DE SILVA AND O. SAVIN and I’m kind of confused of the case k=1.

In the paper they used the Hopf lemma to show that $$u_nu>c>0$$, but, as the boundary regularity is just $$C^{1, alpha}$$, I don’t think that we can directly use Hopf lemma.

I tried to use the transformation of coordinates to do make a better regularity of boundary, but it only works in the divergence form of equations. I have no clue to the non-divergence form. Is there any way to do this estimate?