Counterexample to strong diamagnetism for the magnetic Robin Laplacian

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 $-\infty$.

arXiv commentAdded Reference [11]; modified the formulae in (1.6), (1.10) and (1.13)

References in corpus (6)

• Mean curvature bounds and eigenvalues of Robin Laplacians
• On the third critical field in Ginzburg-Landau theory
• An effective Hamiltonian for the eigenvalue asymptotics of a Robin Laplacian with a large parameter
• Effects of confinement and surface enhancement on superconductivity
• Lack of diamagnetism and the Little-Parks effect
• On the asymptotics of the principal eigenvalue for a Robin problem with a large parameter in planar domains

Cited by in corpus (4)

• On the isoperimetric inequality for the magnetic Robin Laplacian with negative boundary parameter
• Magnetic steps on the threshold of the normal state
• Magnetic confinement for the 3D Robin Laplacian
• Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential (Derivation of the Aharanov-Bohm potential in the Ginzburg-Landau model)