A NOTE ON THE DISCRETE ALEKSANDROV-BAKELMAN MAXIMUM PRINCIPLE

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 t...

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Bibliographic Details
Published in:	Taiwanese journal of mathematics Vol. 4; no. 1; pp. 55 - 64
Main Authors:	Kuo, Hung-Ju, 郭紅珠, Trudinger, Neil S.
Format:	Journal Article
Language:	English
Published:	Mathematical Society of the Republic of China (Taiwan) 01-03-2000
Subjects:	Applied mathematics Coefficients Determinants Differential operators Mathematical constants Mathematical functions Mathematical inequalities Mathematical vectors Maximum principle Research grants
Online Access:	Get full text
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Summary:	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.
ISSN:	1027-5487 2224-6851
DOI:	10.11650/twjm/1500407198