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Approximate Conditions and Passage to the Limit in Sobolev Spaces over Thin and Composite Structures

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Abstract

Approximate properties of variable measures compose a base of the two-scale convergence method with respect to a variable measure, which is used in averaging on periodic thin and composite structures. The paper gives a survey of methods for verifying approximate properties. The main focus is on studying composite measures, which have been little studied.

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Authors and Affiliations

  1. Moscow Institute of Radio Technology, Electronics, and Authomatics, Technical University, Russia

    S. E. Pastukhova

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  1. S. E. Pastukhova
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 16, Partial Differential Equations, 2004.

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Pastukhova, S.E. Approximate Conditions and Passage to the Limit in Sobolev Spaces over Thin and Composite Structures. J Math Sci 133, 931–948 (2006). https://doi.org/10.1007/s10958-006-0026-9

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  • DOI: https://doi.org/10.1007/s10958-006-0026-9

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