Schauder estimates for fully nonlinear elliptic difference operators

Hung Ju Kuo*, Neil S. Trudinger

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)


    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 Holder 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.

    Original languageEnglish
    Pages (from-to)1395-1406
    Number of pages12
    JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
    Issue number6
    Publication statusPublished - 2002


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