Quantitative Schauder estimates for hypoelliptic equations

Abstract: We derive Schauder estimates using ideas from Campanato's approach for a general class of local hypoelliptic operators and non-local kinetic equations. The method covers equations in divergence and non-divergence form. In particular our results are applicable to the inhomogeneous Landau and Boltzmann equation without cut-off. The paper is self-contained.