04-338 W.D. Evans and Roger T. Lewis
Counting Eigenvalues of Biharmonic Operators with Magnetic Fields (234K, PDF) Oct 28, 04
Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

Abstract. An analysis is given of the spectral properties of perturbations of the magnetic bi-harmonic operator $\Delta_A^2$ 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 $\Delta_\ab^2$ which are shown to have a bearing on the limiting cases of embedding theorems for Sobolev spaces $H^2(\R^n)$.

Files: 04-338.src( 04-338.keywords , EvansLewisII-10-15-04.pdf.mm )