# On the discrete maximum principle for parabolic difference operators

- Volume: 27, Issue: 6, page 719-737
- ISSN: 0764-583X

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topKuo, Hung-Ju, and Trudinger, N. S.. "On the discrete maximum principle for parabolic difference operators." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 27.6 (1993): 719-737. <http://eudml.org/doc/193720>.

@article{Kuo1993,

author = {Kuo, Hung-Ju, Trudinger, N. S.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {parabolic difference inequalities; Krylov maximum principle; explicit and implicit difference schemes; random coefficients},

language = {eng},

number = {6},

pages = {719-737},

publisher = {Dunod},

title = {On the discrete maximum principle for parabolic difference operators},

url = {http://eudml.org/doc/193720},

volume = {27},

year = {1993},

}

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

PB - Dunod

VL - 27

IS - 6

SP - 719

EP - 737

LA - eng

KW - parabolic difference inequalities; Krylov maximum principle; explicit and implicit difference schemes; random coefficients

UR - http://eudml.org/doc/193720

ER -

## References

top- [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. Zbl0177.36802MR164135
- [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. Zbl0361.35003MR737190
- [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. Zbl0362.35038MR420016
- [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. Zbl0619.35004MR901759
- [6] H. J. KUO and N. S. TRUDINGER, Linear elliptic difference inequalities with random coefficients, Math. Comp. 1990, 55, pp. 37-53. Zbl0716.39005MR1023049
- [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. Zbl0745.65058MR1149088
- [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. Zbl0050.12501MR52895
- [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). Zbl0596.35008MR821477
- [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. Zbl0581.35027MR790223

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