  This paper studies Schauder theory to transmission problems modelled by fully
nonlinear uniformly elliptic equations of second order. We focus on operators F
that fails to be concave or convex in the space of symmetric matrices. In a
first scenario, it is considered that F enjoys a small ellipticity aperture. In
our second case, we study regularity results where the convexity of the
superlevel (or sublevel) sets is verified, implying that the operator F is
quasiconcave (or quasiconvex).
