= Solution
Let $u\in H^1_{\mathrm{loc}}(\Omega)$ weakly solve
$$
D_i(a^{ij}D_ju)=D_iF^i+g,
$$
where $a^{ij},F^i\in C^{0,\alpha}$, $g\in L^p$ for a suitable $p>n/(1-\alpha)$, and $a^{ij}$ is uniformly elliptic. The interior divergence-form Schauder estimate states that for $\Omega'\Subset\Omega_1\Subset\Omega$,
$$
\boxed{\|u\|_{C^{1,\alpha}(\Omega')}
\leq C\left(\|u\|_{L^2(\Omega_1)}
+\|F\|_{C^{0,\alpha}(\Omega_1)}+\|g\|_{L^p(\Omega_1)}\right).}
$$
For the homogeneous equation the final two terms vanish.
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