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Green’s Function for the Dirichlet Boundary Value Problem in a Domain with Several Inclusions

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Green's Kernels and Meso-Scale Approximations in Perforated Domains

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2077))

Abstract

Here we focus on Green’s kernels of the operator − Δ for the case of the domain containing multiple inclusions. The uniform asymptotic approximations, obtained here, can serve for the evaluation of Green’s function for anti-plane shear in a domain with several inclusions. Formal asymptotic construction has been accompanied by the error estimates for the remainder term.

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Authors and Affiliations

  1. Department of Mathematics, Linköping University, Linköping, Sweden

    Vladimir Maz’ya

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Alexander Movchan

  3. School of Engineering, Liverpool John Moores University, Liverpool, UK

    Michael Nieves

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  1. Vladimir Maz’ya
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  2. Alexander Movchan
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  3. Michael Nieves
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Maz’ya, V., Movchan, A., Nieves, M. (2013). Green’s Function for the Dirichlet Boundary Value Problem in a Domain with Several Inclusions. In: Green's Kernels and Meso-Scale Approximations in Perforated Domains. Lecture Notes in Mathematics, vol 2077. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00357-3_3

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