Local Hölder continuity of weak solutions for an anisotropic elliptic equation

We prove, following DiBenedetto’s intrinsic scaling method, that a local bounded weak solution of the equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\sum_{i=1}^{N}\frac{\partial}{\partial x_i}\left[\left| \frac{\partial u}{\partial x_i} \right|^{p_{i}-2} \frac{\partial u}{\partial x_i} \right]=f $$\end{document}in Ω, is locally Hölder continuous, where f is a given bounded function and pi ≥ 2, for any i = 1, . . . , N.