A Carleson type inequality for fully nonlinear elliptic equations with non-Lipschitz drift term (Q517089)

The paper studies the boundary behavior of the solutions of the fully nonlinear elliptic equation \[ F(D^2u, Du,x)=0 \] with a general drift term satisfying the growth condition \[ |F(0,p,x)|\leq \phi(|p|)\quad \forall\;(x,p)\in {\mathbb R}^N\times{\mathbb R}^N\,. \] The authors elaborate on the non-homogeneous generalized Harnack inequality proved by the second author, to prove a generalized Carleson estimate. Also, boundary Hölder continuity and a boundary Harnack type inequality are obtained.