  In the present paper, we propose the investigation of variable-exponent,
degenerate/singular elliptic equations in non-divergence form. This current
endeavor parallels the by now well established theory of functionals satisfying
nonstandard growth condition, which in particular encompasses problems ruled by
the $p(x)$-laplacian operator. Under rather general conditions, we prove
viscosity solutions to variable exponent fully nonlinear elliptic equations are
locally of class $C^{1,\kappa}$ for a universal constant $0< \kappa < 1$. A key
feature of our estimates is that they do not depend on the modulus of
continuity of exponent coefficients, and thus may be employed to investigate a
variety of problems whose ellipticity degenerates and/or blows-up in a
discontinuous fashion.
