A note on the discrete Aleksandrov-Bakelman maximum principle

Taiwanese Journal of Mathematics

Volumn 4, Issue 1, 2000, Pages 55-64

  Kuo, Hung Ju ^a   Trudinger, Neil S ^b  

^a NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Balanced operator; Discrete Aleksandrov Bakelman maximum principle; Elliptic operator; Monotone operator

Indexed keywords

EID: 0012993479     PISSN: 10275487     EISSN: None     Source Type: Journal    
DOI: 10.11650/twjm/1500407198     Document Type: Article

References (13)

1. I. J. Bakelman, Convex Analysis and Nonlinear Geometric Elliptic Equations, Springer-Verlag, New York, 1994.
2. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer-Verlag, New York, 1983.
3. M. Kocan, Approximation of viscosity solutions of elliptic partial differential equations on minimal grids, Numer. Math. 72 (1995), 73-92.
4. H. J. Kuo and N. S. Trudinger, Linear elliptic difference inequalities with random coefficients, Math. Comp. 55 (1990), 37-53.
5. _, Discrete methods for fully nonlinear elliptic equations, SIAM J. Numer. Anal. 29 (1992), 123-135.
6. _, On the discrete maximum principle for parabolic difference operators, RAIRO Modeĺ. Math. Anal. Numér. 27 (1993), 719-737.
7. _, Local estimates for parabolic difference operators, J. Differential Equations, 122 (1995), 398-413.
8. _, Positive difference operators on general meshes, Duke Math. J. 83 (1996), 415-433.
9. _, Maximum principles for difference operators, in: Topics in Partial Differential Equations & Applications: Collected Papers in Honor of Carlo Pucci, Lecture Notes in Pure and Applied Mathematics Series/177, Marcel Dekker, Inc., 1996, pp. 209-219.
10. _, Evolving monotone difference operators on general space-time meshes, Duke Math. J. 91 (1998), 587-607.
11. K. Leichtweiss, Affine Geometry of Convex Bodies, Barth Verlag, Heidelberg, 1998.
12. R. Sibson, A vector identity for the Dirichlet tessellation, Math. Proc. Cambridge Philos. Soc. 87 (1980), 151-155.
13. N. S. Trudinger, Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations, Invent. Math. 61 (1980), 67-79.