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/