A question about regularity results in the linear Elliptic case which are given by Schauder theory

Question

I've been reading Jost's lecture notes "Nonlinear Methods in Riemannian and Kählerian Geometry". In section 2.2 he gives a regular results about Elliptic and parabolic equations, but he doesn't prove it. And he says we can find elliptic results in "Gilbarg, D., and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Grundlehren 224, Berlin, Heidelberg, New York, 1977" A classic book on elliptic equations. But I did not find a proof of this theorem in this book. So how should I prove this regularity result? Or does anyone know where this theorem comes from?