In this paper we study partial and anisotropic Schauder estimates
for linear and nonlinear elliptic equations. We prove that if the
inhomogeneous term $f$ is Hölder continuous in the
$x_n$-direction, then the mixed derivatives uxxn are Hölder
continuous; if $f$ satisfies an anisotropic Hölder continuity
condition, then the second derivatives $D^2 u$ satisfy related
anisotropic Hölder continuity estimates.