I am reading the book "Elliptic partial differential equations of second order" by D. Gilbarg and N. S. Trudinger.

Specifically, I am interested in Hölder regularity estimates for solution of elliptic problems in divergence form with Hölder coefficients on a domain whose boundary is smooth ($C^2$ for example).

Theorem 8.33 p 210 of this book is exactly what I am looking for. However, the right-hand side of the inequality depends on a constant which depends on the Hölder norms of the coefficients in a non-explicit way. I am looking for any references (or argument) which explicit this constant. In particular, I would like to know what is the dependency on the Hölder norms of the coefficients of the elliptic problem.

For simplicity, I am restating this inequality: \begin{align} |u|_{1,\alpha}\leq C (|u|_0+|g|_0+|f|_{0,\alpha}) \end{align} where $u$ is a $C^{1,\alpha}(\overline{\Omega})$ solution of the elliptic problem \begin{align} L(u)=g+D_if^i, \end{align} with $u=0$ on the boundary, $L=D_i(a^{i,j}(x)D_ju)$, $\max |a^{i,j}|_{0,\alpha}=K<+\infty$ and $C>0$ depending on $K$. I want to know the dependency on $K$ of $C$.

Thanks in advance.