Applications of Functional Equations to Dirichlet Problem for Doubly Connected Domains

Vladimir Mityushev ()
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Vladimir Mityushev: Pedagogical University

A chapter in Handbook of Functional Equations, 2014, pp 315-325 from Springer

Abstract: Abstract The Dirichlet problem with prescribed vortices for the two-dimensional Laplace equation can be considered as a modification of the classical Dirichlet problem. The modified problem for doubly connected circular domains is reduced to the Riemann–Hilbert boundary value problem and solved by iterative functional equations. The solution of functional equations is derived in terms of the absolutely and uniformly convergent series. The obtained solution can be applied to the minimization of the Ginzburg–Landau functional.

Keywords: Multiply connected domain; Riemann-Hilbert boundary value problem; Iterative functional equation; Ginzburg-Landau functional (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1246-9_14

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DOI: 10.1007/978-1-4939-1246-9_14

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