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Algebra i Analiz, 2009, Volume 21, Issue 5, Pages 155–195 (Mi aa1157)  

This article is cited in 7 scientific papers (total in 7 papers)

Research Papers

The Eshelby theorem and the problem on optimal patch

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (435 kB) Citations (7)
References:
Abstract: Let $\Omega^0$ be an ellipsoidal inclusion in the Euclidean space ${\mathbb{R}}^n$. It is checked that if a solution of the homogeneous transmission problem for a formally selfadjoint elliptic system of second order differential equations with piecewise smooth coefficients grows linearly at infinity, then this solution is a linear vector-valued function in the interior of $\Omega^0$. This fact generalizes the classical Eshelby theorem in elasticity theory and makes it possible to indicate simple and explicit formulas for the polarization matrix of the inclusion in the composite space, as well as to solve a problem about optimal patching of an elliptical hole.
Received: 24.03.2009
English version:
St. Petersburg Mathematical Journal, 2010, Volume 21, Issue 5, Pages 791–818
DOI: https://doi.org/10.1090/S1061-0022-2010-01118-X
Bibliographic databases:
Document Type: Article
MSC: 35J57, 74B05
Language: Russian
Citation: S. A. Nazarov, “The Eshelby theorem and the problem on optimal patch”, Algebra i Analiz, 21:5 (2009), 155–195; St. Petersburg Math. J., 21:5 (2010), 791–818
Citation in format AMSBIB
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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