On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk

Astamur Bagapsh and Alexandre Soldatov ()
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Astamur Bagapsh: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 40 Vavilova St., Moscow 119333, Russia
Alexandre Soldatov: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 40 Vavilova St., Moscow 119333, Russia

Mathematics, 2023, vol. 11, issue 20, 1-9

Abstract: The role played by explicit formulas for solving boundary value problems for elliptic equations and systems is well known. In this paper, explicit formulas for a general solution of the Dirichlet problem for second-order elliptic systems in the unit disk are given. In addition, an iterative method for solving this problem for systems with respect to two unknown functions is described, and an integral representation of the Poisson type is obtained by applying this method.

Keywords: Dirichlet problem; second-order elliptic system; integral representation; Poisson integral; unit disk; Fredholm property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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