2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170568We 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.12 pagesMathematical PhysicsAnalysis of PDEs39A12; 39A70text