Boundary regularity of solutions of the fully nonlinear boundary value problem
\[
F
(
x
,
u
,
D
u
,
D
2
u
)
=
0
in
Ω
,
G
(
x
,
u
,
D
u
)
=
0
on
∂
Ω
F(x,u,Du,{D^2}u) = 0\quad {\text {in}}\;\Omega ,\qquad G(x,u,Du) = 0\quad {\text {on}}\;\partial \Omega
\]
is discussed for two-dimensional domains
Ω
\Omega
. The function
F
F
is assumed uniformly elliptic and
G
G
is assumed to depend (in a nonvacuous manner) on
D
u
Du
. Continuity estimates are proved for first and second derivatives of
u
u
under weak hypotheses for smoothness of
F
F
,
G
G
, and
Ω
\Omega
.