On the discrete maximum principle for parabolic difference operators
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 27 (1993) no. 6, pp. 719-737.
@article{M2AN_1993__27_6_719_0,
author = {Kuo, Hung-Ju and Trudinger, N. S.},
title = {On the discrete maximum principle for parabolic difference operators},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
pages = {719--737},
publisher = {AFCET - Gauthier-Villars},
volume = {27},
number = {6},
year = {1993},
zbl = {0787.65059},
mrnumber = {1246996},
language = {en},
url = {http://www.numdam.org/item/M2AN_1993__27_6_719_0/}
}
TY  - JOUR
AU  - Kuo, Hung-Ju
AU  - Trudinger, N. S.
TI  - On the discrete maximum principle for parabolic difference operators
JO  - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY  - 1993
DA  - 1993///
SP  - 719
EP  - 737
VL  - 27
IS  - 6
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1993__27_6_719_0/
UR  - https://zbmath.org/?q=an%3A0787.65059
UR  - https://www.ams.org/mathscinet-getitem?mr=1246996
LA  - en
ID  - M2AN_1993__27_6_719_0
ER  - 
Kuo, Hung-Ju; Trudinger, N. S. On the discrete maximum principle for parabolic difference operators. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 27 (1993) no. 6, pp. 719-737. http://www.numdam.org/item/M2AN_1993__27_6_719_0/

[1] A. D. Aleksandrov, Uniqueness conditions and estimates for the solution of the Dirichlet problem, Vestnik Leningrad. Univ. 18, 1963, no. 3, pp. 5-29, English transl., Amer. Math. Soc. Transl. 1968, 2, 68, pp. 89-119. | MR 164135 | Zbl 0177.36802

[2] I. Ya Bakel'Man, Geometric methods for solving elliptic equations, Nauka, Moscow, 1965 (In Russian).

[3] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, Berlin, Heidelberg, New York and Tokyo, 1983. | MR 737190 | Zbl 0361.35003

[4] N. V. Krylov, Sequence of convex functions and estimates of maximum of the solution of a parabolic equation, Sibirsk Mat. Ž 1976, 17, pp. 290-303 : English translation in Siberian Math. J. 1976, 17, pp. 226-237. | MR 420016 | Zbl 0362.35038

[5] N. V. Krylov, Nonlinear elliptic and parabolic equations of the second order, Nauka, Moscow, 1985 (In Russian). English translation by D. Reidel Publishing Company, Dordrecht, Holland, 1987. | MR 901759 | Zbl 0619.35004

[6] H. J. Kuo and N. S. Trudinger, Linear elliptic difference inequalities with random coefficients, Math. Comp. 1990, 55, pp. 37-53. | MR 1023049 | Zbl 0716.39005

[7] H. J. Kuo and N. S. Trudinger, Discrete methods for fully nonlinear elliptic equations, SIAM J. on Numer. Anal. 1992, 29, pp. 123-135. | MR 1149088 | Zbl 0745.65058

[8] T. Motzkin and W. Wasow, On the approximation of linear elliptic differential equations by difference equations with positive coefficients, J. Math. Phys. 1952, 31, pp. 253-259. | MR 52895 | Zbl 0050.12501

[9] A. I. Nazarov and N. N. Ural Tseva, Convex monotone hulls and estimaties of the maximum of the solution of parabolic equations, Zap. Nauchn Sem. LOMI, 1985, 147, pp. 71-86 (In Russian). | MR 821477 | Zbl 0596.35008

[10] S. J. Reye, Harnack inequalities for parabolic equations in general form with bounded measurable coefficients, Research Report R44-84, Centre for Math. Anal. Aust. Nat. Univ. (1984) (see also Doctoral dissertation : Fully non-linear parabolic differential equations of second order, Aust. Nat. Univ. 1985).

[11] K. Tso, On an Aleksandrov-Bakel'man type maximum principle for second order parabolic equations, Comm. Partial Differential Equations 1985, 10, pp. 543-553. | MR 790223 | Zbl 0581.35027