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

In: Integral Methods in Science and Engineering

Author

Listed:
  • M. Dalla Riva

    (The University of Tulsa, Department of Mathematics)

  • P. Musolino

    (University of Padova, Department of Mathematics)

Abstract

In this survey, we present some recent results obtained by the authors on the asymptotic behavior 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. perforated domain We fix once for all n ∈ ℕ ∖ { 0 , 1 } , α ∈ ] 0 , 1 [ . $$\displaystyle{n \in \mathbb{N}\setminus \{0,1\}\,,\qquad \alpha \in ]0,1[\,.}$$

Suggested Citation

  • M. Dalla Riva & P. Musolino, 2015. "Harmonic Functions in a Domain with a Small Hole: A Functional Analytic Approach," Springer Books, in: Christian Constanda & Andreas Kirsch (ed.), Integral Methods in Science and Engineering, edition 1, chapter 0, pages 143-153, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-16727-5_13
    DOI: 10.1007/978-3-319-16727-5_13
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