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 .
Highlights
1.1 Magnetic Robin LaplacianWe denote by = {x ∈ R2 : |x| < 1} the open unit disc and by = ∂ = {x ∈R2 : |x| = 1} its boundary
We study the lowest eigenvalue of the magnetic Robin
We are interested in examining the asymptotics of the principal eigenvalue λ1(b, γ ) = inf u∈H 1( )
Summary
Ν is the unit outward normal vector of , γ < 0 the Robin parameter and b > 0 is the intensity of the applied magnetic field. The vector field A0 generates the unit magnetic field and is defined as follows. The operator Pγb is defined as the Friedrichs extension, starting from the quadratic form [8, Ch. 4],
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