Partial regularity for elliptic equations

Tian, Guji; Wang, Xu Jia

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Partial regularity for elliptic equations

Date

2010

Authors

Tian, Guji

Wang, Xu Jia

Abstract

In 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 D 2u satisfy related anisotropic Hölder continuity estimates.