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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
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
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
Linking options:
https://www.mathnet.ru/eng/aa1157 https://www.mathnet.ru/eng/aa/v21/i5/p155
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