Gradient estimates for singular fully nonlinear elliptic equations

We study a class of singular fully nonlinear elliptic equations under suitable natural conditions, with the model equation being Δu+b(γ⋅Du)/d−u+c|Du|2=fΔu+b(γ⋅Du)/d−u+c|Du|2=f for Lipschitz functions b>0b>0, cc and ff, where dd denotes distance to the boundary of the domain and γγ is a suitable extension of the interior unit normal. We show that such equations have a unique, globally C1C1 solution (without any a priori prescription of boundary data).