Bounds on resonances for the Laplacian on perturbations of half-space

Authors
Edward, J Pravica, D
Citation
J. Edward et D. Pravica, Bounds on resonances for the Laplacian on perturbations of half-space, SIAM J MATH, 30(6), 1999, pp. 1175-1184
Citations number
23
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN journal
00361410 → ACNP
Volume
30
Issue
6
Year of publication
1999
Pages
1175 - 1184
Database
ISI
SICI code
0036-1410(19991013)30:6<1175:BORFTL>2.0.ZU;2-C
Abstract
The resonances of the Laplacian on perturbations of half-spaces of dimensio ns greater than or equal to two, with either Dirichlet or Neumann boundary conditions, are studied. An upper bound for the resonance counting function is proven. If the domain has an elliptic, nondegenerate, nonglancing perio dic billiard trajectory, it is shown that there exists a sequence of resona nces that converge to the real axis.