On some discrete model of the magnetic Laplacian
Mathematical Physics
2007-05-23 v1 Analysis of PDEs
math.MP
Abstract
We construct some intrinsically defined discrete model of the magnetic Laplacian. The existence and uniqueness of solutions of the Dirichlet problem for the difference Poisson type equation are proved. We study in detail properties of the discrete model including the limiting process in the two-dimensional Euclidean case.
Keywords
Cite
@article{arxiv.math-ph/0410043,
title = {On some discrete model of the magnetic Laplacian},
author = {Volodymyr Sushch},
journal= {arXiv preprint arXiv:math-ph/0410043},
year = {2007}
}
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13 pages