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Asymptotic Expansions of Elastic Fields in Domains with Boundary and Structural Singularities

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Boundary Element Topics

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Abstract

It is well known that the solutions of elliptic boundary value problems in domains with corners, edges and interfaces develop local singularities at these geometrical and structural peculiarities. Based on V.A. Kondratiev’s fundamental work [31], G. Fichera [23, 24], V.A. Kondratiev and O.A. Oleinik [33, 34], V.G. Maz’ya and B.A. Plamenevski [41, 44], M. Dauge [18], V. Kozlov, V.G. Maz’ya and C. Schwab [37], T.V.Petersdorff [53], H.Schmitz, K.Volk and W.L.Wendland [62] and M. Costabel [14] have analyzed the local asymptotic expansion for the elliptic system of elasticity. This local expansion can be obtained by using Mellin transformation with respect to the distance to boundary or structural singularities. The Mellin transformation yields pencils of differential operators depending on a complex parameter. The resulting holomorphic eigenvalue problem provides the basic information on the local asymptotic expansion determined by the distribution of the corresponding eigenvalues and the associated Jordan chains of generalized eigenfunctions.

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  1. A.-M. Sändig
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  2. W. L. Wendland
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Editors and Affiliations

  1. Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany

    Wolfgang L. Wendland

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Sändig, AM., Wendland, W.L. (1997). Asymptotic Expansions of Elastic Fields in Domains with Boundary and Structural Singularities. In: Wendland, W.L. (eds) Boundary Element Topics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60791-2_20

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  • DOI: https://doi.org/10.1007/978-3-642-60791-2_20

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