Author： Kuo Hung-Ju Trudinger Neil S.
Publisher： Royal Society of Edinburgh
ISSN： 1473-7124
Source： Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.132, Iss.6, 2002-12, pp. : 1395-1406
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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.
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