Evolving monotone difference operators on general space-time meshes

Research Report MRR96-033

Evolving monotone difference operators on general space-time meshes

Hung-Ju Kuo and Neil S. Trudinger

Abstract: Following recent work on positive and monotone difference operators on arbitrary discrete subsets of Euclidean space, we consider the analogous situation for space-time meshes and evolving difference operators which are defined as being independent of future time values. In this general framework, we establish discrete analogues of the Krylov maximum principle, the local maximum principles of Gruber and Reye and the Harnack and Holder estimates of Krylov and Safonov for parabolic partial differential operators.

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