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St. Petersburg Mathematical Journal

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Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients


Author: D. Borisov
Translated by: the author
Original publication: Algebra i Analiz, tom 20 (2008), nomer 2.
Journal: St. Petersburg Math. J. 20 (2009), 175-191
MSC (2000): Primary 35B27
DOI: https://doi.org/10.1090/S1061-0022-09-01043-7
Published electronically: January 30, 2009
MathSciNet review: 2423995
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Abstract | References | Similar Articles | Additional Information

Abstract: A singularly perturbed second order elliptic system in the entire space is treated. The coefficients of the systems oscillate rapidly and depend on both slow and fast variables. The homogenized operator is obtained and, in the uniform norm sense, the leading terms of the asymptotic expansion are constructed for the resolvent of the operator described by the system. The convergence of the spectrum is established, and examples are given.


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Additional Information

D. Borisov
Affiliation: Nuclear Physics Institute, Academy of Sciences, 25068 Řež near Prague, Czech Republic, and Bashkir State Pedagogical University, October Revolution Street 3a, 450000 Ufa, Russia
Email: borisovdi@yandex.ru

DOI: https://doi.org/10.1090/S1061-0022-09-01043-7
Keywords: Homogenization of differentiable operators, unbounded domain, fast and slow variables
Received by editor(s): November 30, 2006
Published electronically: January 30, 2009
Additional Notes: This work was supported in part by RFBR (07-01-00037) and by the Czech Academy of Sciences and Ministry of Education, Youth and Sports (LC06002). The author was also supported by Marie Curie International Fellowship within 6th European Community Framework Program (MIF1-CT-2005-006254), by a grant from the 2004 Balzan prize in mathematics, awarded to Pierre Deligne, and by a grant from the Bashkortostan Republic Program for supporting young scientists.
Article copyright: © Copyright 2009 American Mathematical Society

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