Green function for a two-dimensional discrete Laplace-Beltrami operator

Details Green function for a two-dimensional discrete Laplace-Beltrami operator Green function for a two-dimensional discrete Laplace-Beltrami operator

2007-12-12

arxiv.org/abs/0712.2030v1

Cubo 10 (2008), no. 2, 47--59

Physics

Mathematical Physics

12 pages

Scientific paper

We study a discrete model of the Laplacian in $\mathbb{R}^2$ 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.

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