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Partial regularity for elliptic equations

Tian, Guji; Wang, Xu-Jia

Description

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 D²v satisfy related anisotropic Hölder continuity estimates.

CollectionsANU Research Publications
Date published: 2010
Type: Journal article
URI: http://hdl.handle.net/1885/100226
Source: Discrete and Continuous Dynamical Systems
DOI: 10.3934/dcds.2010.28.899

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