Premium
Counting eigenvalues of biharmonic operators with magnetic fields
Author(s) -
Evans W. D.,
Lewis R. T.
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410319
Subject(s) - mathematics , biharmonic equation , eigenvalues and eigenvectors , limiting , mathematical proof , sobolev space , pure mathematics , operator (biology) , embedding , type (biology) , magnetic field , mathematical analysis , physics , quantum mechanics , geometry , chemistry , mechanical engineering , ecology , biochemistry , repressor , artificial intelligence , biology , computer science , transcription factor , engineering , gene , boundary value problem
An analysis is given of the spectral properties of perturbations of the magnetic bi‐harmonic operator Δ 2 A in L 2 ( R n ), 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 Δ 2 A which are shown to have a bearing on the limiting cases of embedding theorems for Sobolev spaces H 2 ( R n ). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom