Let $ \Omega\subset\mathbb{R}^d $ is a $ C^{1,\eta} $ domian with $ 0<\eta<1 $. Assume that $ A(y)=(a_{ij}^{\alpha\beta}(y)) $ is a matrix valued function, where $ 1\leq i,j\leq d $ and $ 1\leq\alpha,\beta\leq m $ with elliptic condition as follows \begin{eqnarray} \lambda|\xi|^2\leq\sum_{i,j,\alpha,\beta}a_{ij}^{\alpha\beta}(y)\xi_{i}^{\alpha}\xi_{j}^{\beta}\leq\lambda^{-1}|\xi|^2 \end{eqnarray} for all $ \xi=(\xi_i^{\alpha})\in\mathbb{R}^{m\times d} $ with constant $ \lambda>0 $. Let $ L=\operatorname{div}(A(x)\nabla) $ be an elliptic operator. Consider the Dirichelt problem as follows \begin{eqnarray} Lu&=&0\text{ in }\Omega,\\ u&=&g\text{ on }\partial\Omega, \end{eqnarray} where $ g\in C^{0,\sigma} $ with $ 0<\sigma<1 $. I want to ask that if I want to get the Schauder types estimates as \begin{eqnarray} \left\|u\right\|_{C^{0,\sigma}(\Omega)}\leq C\left\|g\right\|_{C^{0,\sigma}(\Omega)}, \end{eqnarray} what conditions should I assume for $ A $. The weaker conditions, the better. I have already know that if $ A\in C^{0,\sigma}(\Omega) $, we can get stronger estimates. I wonder if the condition of $ VMO $ is related to this topic.