  In this paper, we prove borderline gradient continuity of viscosity solutions
to Fully nonlinear elliptic equations at the boundary of a
$C^{1,\dini}$-domain. Our main result Theorem 3.1 is a sharpening of the
boundary gradient estimate proved by Ma-Wang following the borderline interior
gradient regularity estimates established Daskalopoulos-Kuusi-Mingione. We
however mention that, differently from the approach in the interior case which
depends on $W^{1,q}$ estimates, our proof is slightly more geometric and is
based on compactness arguments inspired by the techniques in the fundamental
works of Caffarelli.
