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Schauder estimates for fully nonlinear elliptic difference operators

Published online by Cambridge University Press:  12 July 2007

Hung-Ju Kuo  and
Neil S. Trudinger
Hung-Ju Kuo
Affiliation:
Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan ([email protected])
Neil S. Trudinger
Affiliation:
Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia ([email protected])
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Abstract

In this paper, we are concerned with discrete Schauder estimates for solutions of fully nonlinear elliptic difference equations. Our estimates are discrete versions of second derivative Hölder estimates of Evans, Krylov and Safonov for fully nonlinear elliptic partial differential equations. They extend previous results of Holtby for the special case of functions of pure second-order differences on cubic meshes. As with Holtby's work, the fundamental ingredients are the pointwise estimates of Kuo-Trudinger for linear difference schemes on general meshes.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 6 , December 2002 , pp. 1395 - 1406
Copyright
Copyright © Royal Society of Edinburgh 2002

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