Partial regularity for elliptic equations

Tian, Guji; Wang, Xu-Jia

Cultural advice

The Australian National University acknowledges, celebrates and pays our respects to the Ngunnawal and Ngambri people of the Canberra region and to all First Nations Australians on whose traditional lands we meet and work, and whose cultures are among the oldest continuing cultures in human history.

Aboriginal and Torres Strait Islander peoples are advised that ANU Library collections may include images, names, voices, and other representations of deceased persons.

Material in the collection may contain terms, language or views that reflect the period in which the item was created and may be considered inappropriate today.

Partial regularity for elliptic equations

Date

2010

Authors

Tian, Guji

Wang, Xu-Jia

Publisher

American Institute of Mathematical Sciences

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 D²v satisfy related anisotropic Hölder continuity estimates.