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)

Homogenization with corrector term for periodic elliptic differential operators


Authors: M. Sh. Birman and T. A. Suslina
Translated by: T. A. Suslina
Original publication: Algebra i Analiz, tom 17 (2005), nomer 6.
Journal: St. Petersburg Math. J. 17 (2006), 897-973
MSC (2000): Primary 35J99
Published electronically: September 21, 2006
MathSciNet review: 2202045
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We continue to study the class of matrix periodic elliptic differential operators $ {{\mathcal{A}}_\varepsilon}$ in $ {\mathbb{R}^d}$ with coefficients oscillating rapidly (i.e., depending on $ {{\mathbf{x}}/\varepsilon}$). This class was introduced in the authors' earlier work of 2001 and 2003. The problem of homogenization in the small period limit is considered. Approximation for the resolvent $ {({\mathcal{A}}_\varepsilon + I)^{-1}}$ is obtained in the operator norm in $ {L_2(\mathbb{R}^d)}$ with error term of order $ {\varepsilon^2}$. The so-called corrector is taken into account. We develop the approach of our paper of 2003, where approximation with no corrector term but with remainder term of order $ {\varepsilon}$ was found. The paper is based on the operator-theoretic material obtained in our paper in the previous issue of this journal. Though the present paper is a continuation of the earlier work, it can be read independently.


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


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 35J99

Retrieve articles in all journals with MSC (2000): 35J99


Additional Information

M. Sh. Birman
Affiliation: Department of Physics, St. Petersburg State University, Ulyanovskaya 1, Petrodvorets, St. Petersburg 198504, Russia
Email: mbirman@list.ru

T. A. Suslina
Affiliation: Department of Physics, St. Petersburg State University, Ulyanovskaya 1, Petrodvorets, St. Petersburg 198504, Russia

DOI: http://dx.doi.org/10.1090/S1061-0022-06-00935-6
PII: S 1061-0022(06)00935-6
Keywords: Periodic operators, threshold approximations, homogenization, corrector
Received by editor(s): October 17, 2005
Published electronically: September 21, 2006
Additional Notes: Supported by RFBR (grant nos. 05-01-01076-a and 05-01-02944-YaF-a)
Article copyright: © Copyright 2006 American Mathematical Society