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|標題:||A note on the discrete Aleksandrov-Bakelman maximum principle||作者:||Kuo, H.J.
|關鍵字:||discrete Aleksandrov-Bakelman maximum principle;balanced operator;monotone operator;elliptic operator;parabolic difference-operators;equations;meshes||Project:||Taiwanese Journal of Mathematics||期刊/報告no：:||Taiwanese Journal of Mathematics, Volume 4, Issue 1, Page(s) 55-64.||摘要:||
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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