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.
Exact solution to the Dirichlet problem for degenerating on the boundary elliptic equation of Tricomi-Keldysh type in the half-space
Construction by similarity method of the fundamental solution of the Dirichlet problem for Keldysh type equation in the half-space
Counting function of the embedded eigenvalues for some manifold with cusps, and magnetic Laplacian
