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math.SP2024
On the Laplace operator with a weak magnetic field in exterior domains
Ayman Kachmar, Vladimir Lotoreichik, Mikael Sundqvist
We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate…
math.SP2024
Inequalities between Dirichlet and Neumann eigenvalues of the magnetic Laplacian
Vladimir Lotoreichik
We consider the magnetic Laplacian with the homogeneous magnetic field in two and three dimensions. We prove that the -th magnetic Neumann eigenvalue of a bounded convex pla…
math.AP2024
Homogenization of the Dirac operator with position-dependent mass
Andrii Khrabustovskyi, Vladimir Lotoreichik
We address the homogenization of the two-dimensional Dirac operator with position-dependent mass. The mass is piecewise constant and supported on small pairwise disjoint inclusions…