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Harmonic Functions in a Domain with a Small Hole: A Functional Analytic Approach

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Integral Methods in Science and Engineering

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Abstract

In this survey, we present some recent results obtained by the authors on the asymptotic behavior of harmonic functions in a bounded domain with a small hole. Particular attention will be paid to the case of the solutions of a Dirichlet problem for the Laplace operator in a perforated domain. We fix once for all

$$\displaystyle{n \in \mathbb{N}\setminus \{0,1\}\,,\qquad \alpha \in ]0,1[\,.}$$

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Acknowledgements

The research of M. Dalla Riva was supported by Portuguese funds through the CIDMA—Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013. The research of M. Dalla Riva was also supported by the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”) with the research grant SFRH/BPD/ 64437/2009. P. Musolino is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The work of M. Dalla Riva and P. Musolino is also supported by “Progetto di Ateneo: Singular perturbation problems for differential operators – CPDA120171/12” of the University of Padova.

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Authors and Affiliations

  1. Department of Mathematics, The University of Tulsa, Tulsa, OK, USA

    M. Dalla Riva

  2. Department of Mathematics, University of Padova, Padova, Italy

    P. Musolino

Authors
  1. M. Dalla Riva
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  2. P. Musolino
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Corresponding author

Correspondence to P. Musolino .

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Editors and Affiliations

  1. Department of Mathematics, The University of Tulsa, Department of Mathematics, Oklahoma, Oklahoma, USA

    Christian Constanda

  2. Department of Mathematics, Karlsruhe Institute of Technology, Department of Mathematics, Karlsruhe, Germany

    Andreas Kirsch

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Riva, M.D., Musolino, P. (2015). Harmonic Functions in a Domain with a Small Hole: A Functional Analytic Approach. In: Constanda, C., Kirsch, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16727-5_13

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