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Non-monotonicity for the 3D magnetic Robin Laplacian

2022/02/02 by Germán Miranda, Miranda, Germán
Computer Science · Mathematics · #35P05 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2202.01001

openalex publication_date 2022/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Previous 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 Robin magnetic 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 +∞.

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