Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On the spectrum of the Laplace operator on the infinite Dirichlet ladder


Author: S. A. Nazarov
Translated by: A. I. Plotkin
Original publication: Algebra i Analiz, tom 23 (2011), nomer 6.
Journal: St. Petersburg Math. J. 23 (2012), 1023-1045
MSC (2010): Primary 35J05
Published electronically: September 17, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The spectrum of the Dirichlet problem is studied in the case of a periodic infinite planar domain having the form of an accommodation ladder: two parallel strips-uprights of thickness $ h>0$ are linked by treads of the same thickness. It is shown that, for $ h$ small, a gap is always opened between the second and third segments of the essential spectrum of the problem operator. The gap between the first and second segments is also discussed: its presence and characteristics depend on the distance between the uprights. It is shown that variation of the thickness of finitely many treads leads to the arising of any prescribed number of discrete spectrum points below the essential spectrum as well as inside the open gap.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 35J05

Retrieve articles in all journals with MSC (2010): 35J05


Additional Information

S. A. Nazarov
Affiliation: Institute of Mechanical Engineering Problems, Bol’shoĭ pr. V.O. 61, 199178 St.Petersburg, Russia
Email: srgnazarov@yahoo.co.uk

DOI: http://dx.doi.org/10.1090/S1061-0022-2012-01228-8
PII: S 1061-0022(2012)01228-8
Keywords: Periodic junction of thin domains, essential spectrum, Dirichlet problem, gaps, discrete spectrum
Received by editor(s): January 25, 2010
Published electronically: September 17, 2012
Additional Notes: Supported by RFBR (grant no. 09-01-00759)
Article copyright: © Copyright 2012 American Mathematical Society