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 Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 1, Pages 126–144 (Mi zvmmf722)

Asymptotics of a reduced logarithmic capacity

I. I. Argatov

Abstract: The homogeneous Dirichlet problem for the Laplace operator in a layer with a hole $G$ is considered. Periodicity conditions are imposed on the planes of the layer. A solution is sought in the class of functions that increase logarithmically at infinity. The reduced logarithmic capacity of the closed domain $\overline G$ is defined as a generalization of the logarithmic capacity (the outer conformal radius) of a closed plane domain. Formal asymptotics are constructed for the following shapes of $G$: an almost cylindrical domain, a thin cylinder of low height, a domain of small diameter, and a narrow cylinder of small thickness.

Key words: logarithmic capacity, Dirichlet problem for the Laplace operator, asymptotic behavior of a solution.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:1, 120–137

Bibliographic databases:
UDC: 519.634

Citation: I. I. Argatov, “Asymptotics of a reduced logarithmic capacity”, Zh. Vychisl. Mat. Mat. Fiz., 45:1 (2005), 126–144; Comput. Math. Math. Phys., 45:1 (2005), 120–137

Citation in format AMSBIB
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