Ukrainian Mathematical Bulletin

Volume 2, Issue 4, 2005 pp. 591-607.

On Some Discrete Model of Magnetic Laplacian

Authors: Volodymyr N. Sushch
Author institution: Volodymyr N. Sushch, Politechnika Koszalinska 2, Sniadeckich, 75-453, Koszalin, Poland; Ya.S.Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of NAS of Ukraine, 3-b Naukova Str., 79000, Lviv, Ukraine sushch@tu.koszalin.pl

Summary: We construct a discrete model of a magnetic Laplacian that preserves the geometric structure of the corresponding continual object. We prove a theorem on the existence and uniqueness of a solution of the Dirichlet problem for a difference equation of the Poisson type. In the two-dimensional Euclidean case, we thoroughly study the properties of the discrete model, including approximation and limit transition.

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