Duke Mathematical Journal

Evolving monotone difference operators on general space-time meshes

Hung-Ju Kuo and Neil S. Trudinger

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Duke Math. J., Volume 91, Number 3 (1998), 587-607.

First available in Project Euclid: 19 February 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65M06: Finite difference methods
Secondary: 35K10: Second-order parabolic equations 39A70: Difference operators [See also 47B39] 65M12: Stability and convergence of numerical methods


Kuo, Hung-Ju; Trudinger, Neil S. Evolving monotone difference operators on general space-time meshes. Duke Math. J. 91 (1998), no. 3, 587--607. doi:10.1215/S0012-7094-98-09122-0. https://projecteuclid.org/euclid.dmj/1077232259

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  • [1] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983.
  • [2] M. Gruber, Harnack inequalities for solutions of general second order parabolic equations and estimates of their Hölder constants, Math. Z. 185 (1984), no. 1, 23–43.
  • [3] M. Kocan, Approximation of viscosity solutions of elliptic partial differential equations on minimal grids, Numer. Math. 72 (1995), no. 1, 73–92.
  • [4] N. V. Krylov, Sequences of convex functions, and estimates of the maximum of the solution of a parabolic equation, Sibirsk. Mat. Ž. 17 (1976), no. 2, 290–303, 478, Siberian Math. J. 17 (1976), 226–237 (English trans.).
  • [5] N. V. Krylov and M. V. Safonov, A property of the solutions of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), no. 1, 161–175, 239, Math. USSR-Izv. 16 (1981), 151–164.
  • [6] H.-J. Kuo and N. S. Trudinger, Linear elliptic difference inequalities with random coefficients, Math. Comp. 55 (1990), no. 191, 37–53.
  • [7] H.-J. Kuo and N. S. Trudinger, Discrete methods for fully nonlinear elliptic equations, SIAM J. Numer. Anal. 29 (1992), no. 1, 123–135.
  • [8] H.-J. Kuo and N. S. Trudinger, On the discrete maximum principle for parabolic difference operators, RAIRO Modél. Math. Anal. Numér. 27 (1993), no. 6, 719–737.
  • [9] H.-J. Kuo and N. S. Trudinger, Local estimates for parabolic difference operators, J. Differential Equations 122 (1995), no. 2, 398–413.
  • [10] H.-J. Kuo and N. S. Trudinger, Positive difference operators on general meshes, Duke Math. J. 83 (1996), no. 2, 415–433.
  • [11] H.-J. Kuo and N. S. Trudinger, Maximum principles for difference operators, Partial differential equations and applications, Lecture Notes in Pure and Appl. Math., vol. 177, Dekker, New York, 1996, pp. 209–219.
  • [12] A. I. Nazarov and N. N. Ural'tseva, Convex-monotone hulls and an estimate of the maximum of the solution of a parabolic equation, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 147 (1985), 95–109, 204–205.
  • [13] S. J. Reye, Harnack inequalities for parabolic equations in general form with bounded measurable coefficients R44-84, Centre for Math. Anal. Australian Nat. Univ., 1984, Fully non-linear parabolic differential equations of second order, Ph.D. dissertation, Australian Nat. Univ., 1985.
  • [14] R. Sibson, A vector identity for the Dirichlet tessellation, Math. Proc. Cambridge Philos. Soc. 87 (1980), no. 1, 151–155.
  • [15] N. S. Trudinger, Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations, Invent. Math. 61 (1980), no. 1, 67–79.
  • [16] K. Tso, On an Aleksandrov-Bakel'man type maximum principle for second-order parabolic equations, Comm. Partial Differential Equations 10 (1985), no. 5, 543–553.