Local regularity for an anisotropic elliptic equation

We establish the interior Hölder continuity for locally bounded solutions, and the Harnack inequality for non-negative continuous solutions to a class of anisotropic elliptic equations with bounded and measurable coefficients, whose prototype equation is $u_{xx} + Delta _{q,y}u= 0$ locally in $R imes R^{N−1}$, for $q < 2$, via ideas and tools originating from the regularity theory for degenerate and singular parabolic equations.