We study a discrete model of the Laplacian in ℝ2 that preserves the geometric structure of the original continual object. This means that, speaking of a discrete model, we do not mean just the direct replacement of differential operators by difference ones but also a discrete analog of the Riemannian structure. We consider this structure on the appropriate combinatorial analog of differential forms. Self-adjointness and boundness for a discrete Laplacian are proved. We define the Green function for this operator and also derive an explicit formula of the one.
@article{1515,
title = {Green Function for a Two-Dimensional Discrete Laplace-Beltrami Operator},
journal = {CUBO, A Mathematical Journal},
volume = {10},
year = {2008},
language = {en},
url = {http://dml.mathdoc.fr/item/1515}
}
Sushch, Volodymyr. Green Function for a Two-Dimensional Discrete Laplace-Beltrami Operator. CUBO, A Mathematical Journal, Tome 10 (2008) . http://gdmltest.u-ga.fr/item/1515/