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Counterexample to strong diamagnetism for the magnetic Robin Laplacian. (English) Zbl 1450.35198

Summary: 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 \(-\infty\).

MSC:

35P15 Estimates of eigenvalues in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
47A10 Spectrum, resolvent
47F05 General theory of partial differential operators
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