Explicit bound for $C^{2,\alpha}$ elliptic theory

Question

Let $\Omega$ be an open, bounded with $C^2$ boundary (or smooth as we want). A result about elliptic regularity is given as follows. If $\Omega_0\subset\subset \Omega$ and $u$ is a weak solution of $Lu = f$, where $L$ is uniformly elliptic, then $$ f\in \mathrm{C}(\overline{\Omega}) \quad\Longrightarrow \quad u\in \mathrm{C}^{1,\alpha}$$ for all $\alpha \in (0,1)$ and furthermore there is a constant $C$ such that $$ \Vert u\Vert_{C^{1,\alpha}} \leq C(\Vert u\Vert_{L^2} + \Vert f\Vert_{C(\Omega)})$$ My question is, let us say $L = -\epsilon \Delta$, what is the explicit dependence of the constant $C$ above? If $f$ is nicer, can we get bound $C^{2,\alpha}$ for explicitly too?