- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:14
Journal of Spectral Theory
J. Spectr. Theory
JST
1664-039X
1664-0403
Quantum theory
10.4171/JST
http://www.ems-ph.org/doi/10.4171/JST
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Zuerich, Switzerland
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3
2013
4
Spectral estimates for Dirichlet Laplacians and Schrödinger operators on geometrically nontrivial cusps
Pavel
Exner
Mathematical Physics and Applied Mathematics, PRAGUE, CZECH REPUBLIC
Diana
Barseghyan
Mathematical Physics and Applied Mathematics, PRAGUE, CZECH REPUBLIC
Dirichlet Laplacian, cusp-shaped region, Lieb–Thirring inequalities, bending and twisting
The goal of this paper is to derive estimates of eigenvalue moments for Dirichlet Laplacians and Schrödinger operators in regions having infinite cusps which are geometrically nontrivial being either curved or twisted; we are going to show how those geometric properties enter the eigenvalue bounds. The obtained inequalities reflect the essentially one-dimensional character of the cusps and we give an example showing that in an intermediate energy region they can be much stronger than the usual semiclassical bounds.
Partial differential equations
Operator theory
Quantum theory
465
484
10.4171/JST/51
http://www.ems-ph.org/doi/10.4171/JST/51