Non-monotonicity of the first eigenvalue for the 3D magnetic Robin Laplacian

Abstract

AbstractPrevious works provided several counterexamples to monotonicity of the lowest eigenvalue for the magnetic Laplacian in the two-dimensional case. However, the three-dimensional case is less studied. We use the results obtained by Helffer, Kachmar, and Raymond to provide one of the first counterexamples in 3D. Considering the magnetic Robin Laplacian on the unit ball with a constant magnetic field, we show the non-monotonicity of the lowest eigenvalue asymptotics when the Robin parameter tends to $$+\infty $$ + ∞ .