Continuity of weak solutions of elliptic partial differential equations (Q1426916)

Consider the following nonlinear elliptic equation \[ \operatorname{div} \mathcal A(x,\nabla u)=0 \quad\text{in }\;\Omega, \] where \(A:\Omega\times\mathbb R^n \to\mathbb R^n\) satisfies \(\alpha(x)| \xi| ^p\leq A(x,\xi)\cdot\xi \leq\beta(x)| \xi| ^p\) for some \(1<p\leq n\) and \(\alpha,\beta:\Omega\to\mathbb R_+\). The author proves that the weakly monotone solutions, i.e. solutions satisfying the maximum principle, are continuous if \(\beta/\alpha\) is upper bounded in certain sense.