Displaying similar documents to “Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint”

Local minimizers with vortex filaments for a Gross-Pitaevsky functional

Robert L. Jerrard (2007)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

This paper gives a rigorous derivation of a functional proposed by Aftalion and Rivière [ (2001) 043611] to characterize the energy of vortex filaments in a rotationally forced Bose-Einstein condensate. This functional is derived as a -limit of scaled versions of the Gross-Pitaevsky functional for the wave function of such a condensate. In most situations, the vortex filament energy functional is either unbounded below or has only trivial minimizers, but we establish...

Spectrum of the weighted Laplace operator in unbounded domains

Alexey Filinovskiy (2011)

Mathematica Bohemica

Similarity:

We investigate the spectral properties of the differential operator - r s Δ , s 0 with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm u L 2 , s ( Ω ) 2 = Ω r - s | u | 2 d x , we study the structure of the spectrum with respect to the parameter s . Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.