Abstract
We determine a counterexample to strong diamagnetism for the Laplace operator in the unit disc with a uniform magnetic field and Robin boundary condition. The example follows from the accurate asymptotics of the lowest eigenvalue when the Robin parameter tends to \(-\infty \).
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Acknowledgments
This work started when A. Kachmar visited the mathematics department in Lund University. The research of A. Kachmar is supported by a grant from the Lebanese university within the project “Analytical and numerical aspects of the Ginzburg–Landau model”. The authors thank the anonymous referee for valuable comments and suggestions.
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Kachmar, A., Sundqvist, M.P. Counterexample to Strong Diamagnetism for the Magnetic Robin Laplacian. Math Phys Anal Geom 23, 27 (2020). https://doi.org/10.1007/s11040-020-09350-6
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DOI: https://doi.org/10.1007/s11040-020-09350-6