Local estimates for parabolic difference operators
The authors prove a local maximum principle and a weak Harnack inequality for parabolic difference inequalities. As applications, they derive discrete analogues of the Hölder and Harnack estimates of \textit{N. V. Krylov} and \textit{M. V. Safonov} [Izv. Akad. Nauk SSSR, Ser. Mat. 44, 161-175 (1980; Zbl 0439.35023)] and results pertaining to the stability of discrete schemes for nonlinear parabolic problems. For related results see the papers of \textit{M. Gruber} [Math. Z. 185, 23-43 (1984; Zbl 0517.35042)] and the authors [SIAM J. Numer. Anal. 29, No. 1, 123-135 (1992; Zbl 0745.65058)].
scientific article; zbMATH DE number 823555