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

M. Dalla Riva () and P. Musolino ()
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M. Dalla Riva: The University of Tulsa, Department of Mathematics
P. Musolino: University of Padova, Department of Mathematics

Chapter Chapter 13 in Integral Methods in Science and Engineering, 2015, pp 143-153 from Springer

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

Keywords: Harmonic Function; Dirichlet Problem; Laplace Operator; Small Hole; Stoke Flow (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-16727-5_13

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DOI: 10.1007/978-3-319-16727-5_13

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