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St. Petersburg Mathematical Journal

Published by the American Mathematical Society, the St. Petersburg Mathematical Journal (SPMJ) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.54.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions
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by V. G. Maz′ya, A. B. Movchan and M. J. Nieves PDF
St. Petersburg Math. J. 32, 551-564 Request permission


Formal asymptotic algorithms are considered for a class of meso-scale approximations for problems of vibration of elastic membranes that contain clusters of small inertial inclusions distributed along contours of predefined smooth shapes. Effective transmission conditions have been identified for inertial structured interfaces, and approximations to solutions of eigenvalue problems have been derived for domains containing lower-dimensional clusters of inclusions.
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Additional Information
  • V. G. Maz′ya
  • Affiliation: Department of Mathematics, Linköping University, Linköping S–581 83, Sweden; Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom; and RUDN University, 6 Miklukho-Maklay St, 117198 Moscow, Russia
  • MR Author ID: 196507
  • Email:,
  • A. B. Movchan
  • Affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom
  • Email:
  • M. J. Nieves
  • Affiliation: School of Computing and Mathematics, Keele University, Staffordshire, ST5 5BG, United Kingdom; and Department of Mechanical, Chemical and Material Engineering, University of Cagliari, 09123 Cagliari, Italy
  • Email:
  • Received by editor(s): May 11, 2019
  • Published electronically: May 11, 2021
  • Additional Notes: The first author acknowledges that this publication has been prepared with the support of the “RUDN University Program 5-100.” The second author would like to thank the EPSRC (UK) for its support through the Programme Grant no. EP/L024926/1. The third author gratefully acknowledges the support of the EU H2020 grant MSCA-IF-2016-747334-CAT-FFLAP.

  • Dedicated: In honour of Professor N. N. Ural’tseva.
  • © Copyright 2021 American Mathematical Society
  • Journal: St. Petersburg Math. J. 32, 551-564
  • MSC (2020): Primary 74K15
  • DOI:
  • MathSciNet review: 4099100