Inequalities between Dirichlet and Neumann eigenvalues of the magnetic
Laplacian
Inequalities between Dirichlet and Neumann eigenvalues of the magnetic
Laplacian
We consider the magnetic Laplacian with the homogeneous magnetic field in two and three dimensions. We prove that the $(k+1)$-th magnetic Neumann eigenvalue of a bounded convex planar domain is not larger than its $k$-th magnetic Dirichlet eigenvalue. In three dimensions, we restrict our attention to convex domains, which are …