Generalized local maximum principles for finite-difference operators

Author:
Achi Brandt

Journal:
Math. Comp. **27** (1973), 685-718

MSC:
Primary 65Q05

DOI:
https://doi.org/10.1090/S0025-5718-1973-0329289-6

MathSciNet review:
0329289

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Abstract | References | Similar Articles | Additional Information

Abstract: The generalized local maximum principle for a difference operator asserts that if then cannot attain its positive maximum at the net-point *x*. Here is a local net-operator such that for any smooth function *u*. This principle, with simple forms of , is proved for some quite general classes of second-order elliptic operators , whose associated global matrices are not necessarily monotone. It is shown that these generalized principles can be used for easy derivation of global a priori estimates to the solutions of elliptic difference equations and to their difference-quotients. Some examples of parabolic difference equations are also treated.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0329289-6

Keywords:
Elliptic difference operators,
parabolic difference operators,
boundary value problems,
maximum principles,
monotone matrices,
a priori estimates,
estimates for difference-quotients

Article copyright:
© Copyright 1973
American Mathematical Society