Spectral estimates for Dirichlet Laplacians and Schrodinger operators on geometrically nontrivial cusps

0435960 - ÚJF 2015 RIV CH eng J - Článek v odborném periodiku
Exner, Pavel - Barseghyan, Diana
Spectral estimates for Dirichlet Laplacians and Schrodinger operators on geometrically nontrivial cusps.
Journal of Spectral Theory. Roč. 3, č. 4 (2013), s. 465-484. ISSN 1664-039X. E-ISSN 1664-0403
Grant CEP: GA ČR GAP203/11/0701
Institucionální podpora: RVO:61389005
Klíčová slova: Dirichlet Laplacian * cusp-shaped region * Lieb-Thirring inequalities * bending and twisting
Kód oboru RIV: BE - Teoretická fyzika

The goal of this paper is to derive estimates of eigenvalue moments for Dirichlet Laplacians and Schrodinger 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.
Trvalý link: http://hdl.handle.net/11104/0239808