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 Mat. Zametki, 2001, Volume 69, Issue 6, Pages 876–891 (Mi mz701)

The Mixed Problem for the Laplace Equation in an Exterior Domain with an Arbitrary Partition of the Boundary

P. A. Krutitskii

M. V. Lomonosov Moscow State University

Abstract: In this paper we propose a method for solving the mixed boundary-value problem for the Laplace equation in a connected exterior domain with an arbitrary partition of the boundary. All simple closed curves making up the boundary are divided into three sets. On the elements of the first set the Dirichlet condition is given, on the elements of the second set the third boundary condition is prescribed, and the third set, in turn, is divided into two subsets of simple closed arcs, with the Dirichlet condition prescribed on the elements of one of these subsets and the third boundary condition on the elements of the other subset. The problem is reduced to a uniquely solvable Fredholm equation of the second kind in a Banach space. The third boundary-value problem and the mixed Dirichlet–Neumann problem are particular cases of the problem under study.

DOI: https://doi.org/10.4213/mzm701

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English version:
Mathematical Notes, 2001, 69:6, 799–813

Bibliographic databases:

UDC: 517.9
Revised: 23.08.1999

Citation: P. A. Krutitskii, “The Mixed Problem for the Laplace Equation in an Exterior Domain with an Arbitrary Partition of the Boundary”, Mat. Zametki, 69:6 (2001), 876–891; Math. Notes, 69:6 (2001), 799–813

Citation in format AMSBIB
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This publication is cited in the following articles:
1. Wang J., Zhang L., Ma F., “Finite Element Method With Nonlocal Boundary Condition For Solving the Nondestructive Testing Problem of Wood Moisture Content”, Appl. Math. Comput., 250 (2015), 432–443
2. Torebek B.T., Turmetov B.Kh., “On solvability of exterior boundary value problem with fractional boundary condition”, ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences (Antalya, Turkey, 5?7 November 2015), AIP Conference Proceedings, 1676, eds. Ashyralyev A., Malkowsky E., Lukashov A., Basar F., Amer Inst Physics, 2015, 020096
3. Torebek B.T., Turmetov B.Kh., “Questions on solvability of exterior boundary value problems with fractional boundary conditions”, Electron. J. Qual. Theory Differ., 2016, no. 25
4. Corfdir A., Bonnet G., “Degenerate Scale For 2D Laplace Equation With Mixed Boundary Condition and Comparison With Other Conditions on the Boundary”, Eng. Anal. Bound. Elem., 88 (2018), 14–25
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