TAIWANESE JOURNAL OF MATHEMATICS

Vol. 4, No. 1, pp. 55-64,  March 2000

　

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    A NOTE ON THE DISCRETE ALEKSANDROV-BAKELMAN MAXIMUM PRINCIPLE

　

Hung-Ju Kuo* and Neil S. Trudinger**
　

Abstract.
              In previous works, we have established discrete versions of the Aleksandrov-Bakelman maximum principle for elliptic operators, on general meshes in Euclidean space. In this paper, we prove a variant of these estimates in terms of a discrete analogue of the determinant of the coefficient matrix in the differential operator case. Our treatment depends on an interesting connection between the determinant and volumes of cells in the underlying mesh.

　

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Received November 19, 1999.

Communicated by P. Y. Wu.

2000 Mathematics Subject Classification: Primary 65N12, 35J15, 39A70; Secondary 65N40, 35B05, 39A10.

Key words and phrases: Discrete Aleksandrov-Bakelman maximum principle, balanced operator, monotone operator, elliptic operator.

* Research supported by Taiwan National Science Council under Grant No. NSC37155F.

** Research supported by Australian Research Council Grant.