Holder estimates for the gradient of the solutions to the linear divergence form elliptic equation?

Question

Now I'm considering the Drichlet problem \begin{align} (a_{ij}(x)u_{x_i})_{x_j}+b_i(x)u_{x_i}+c(x)u &= f(x),\quad x\text{ in }\Omega \\ u(x) &= g(x),\quad x\text{ on } \partial \Omega.\tag{1} \end{align} I need some results about the gradient holder estimates of the weak solution under the appropriate smoothness assumption on the coefficients and data,but $a_{ij}$ must be in $C^{\alpha}(\bar\Omega)$ only. Such as the form as follows

$$||Du||_{C^{\alpha}(\bar\Omega)}\leq C(\text{depends on what?})(||u||_{C(\bar\Omega)}+||g||_{X}+||f||_Y).\tag{2}$$

Any answer and reference is appreciated! :)

Answer 1

At the suggestion of 5pm，I find the result in chapter 8,section 8.11 of the book "Elliptic Partial Differential Equations of Second Order" by Gilbarg and Trudinger.