Counting eigenvalues of biharmonic operators with magnetic fields

Academic Article


  • An analysis is given of the spectral properties of perturbations of the magnetic bi-harmonic operator ΔA2 in L 2(Rn), n = 2, 3, 4, where A is a magnetic vector potential of Aharonov-Bohm type, and bounds for the number of negative eigenvalues are established. Key elements of the proofs are newly derived Rellich inequalities for ΔA2 which are shown to have a bearing on the limiting cases of embedding theorems for Sobolev spaces H2(R n). © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Evans WD; Lewis RT
  • Start Page

  • 1524
  • End Page

  • 1537
  • Volume

  • 278
  • Issue

  • 12-13