Counting eigenvalues of biharmonic operators with magnetic fields

Autor:	William Desmond Evans, R. T. Lewis
Rok vydání:	2005
Předmět:	Sobolev space Pure mathematics Operator (computer programming) General Mathematics Mathematical analysis Biharmonic equation Embedding Magnetic potential Type (model theory) Eigenvalues and eigenvectors Mathematics Magnetic field
Zdroj:	Mathematische Nachrichten. 278:1524-1537
ISSN:	1522-2616 0025-584X
DOI:	10.1002/mana.200410319
Popis:	An analysis is given of the spectral properties of perturbations of the magnetic bi-harmonic operator Δ2A in L2(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 Δ2A which are shown to have a bearing on the limiting cases of embedding theorems for Sobolev spaces H2(Rn). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Databáze:	OpenAIRE
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