Tian, GujiWang, Xu-Jia2016-03-112016-03-111078-0947http://hdl.handle.net/1885/100226In this paper we study partial and anisotropic Schauder estimates for linear and nonlinear elliptic equations. We prove that if the inhomogeneous term f is Hölder continuous in the Xn-direction, then the mixed derivatives uxxn are Hölder continuous; if f satisfies an anisotropic Hölder continuity condition, then the second derivatives D²v satisfy related anisotropic Hölder continuity estimates.The first author was supported by NSFC Grant 10871199. The second author was supported by the Australian Research Council.© American Institute of Mathematical Sciences.Keywords: Elliptic equation; Partial regularity; Perturbation argument201010.3934/dcds.2010.28.8992016-06-14