Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Aldashev S. A. Nonlocal Boundary-Value Problems in the Cylindrical Domain for the Multidimensional Laplace Equation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2019, vol. 19, iss. 1, pp. 16-23. DOI: 10.18500/1816-9791-2019-19-1-16-23, EDN: OJMZIH

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
28.02.2019
Full text:
(downloads: 188)
Language: 
Russian
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Article type: 
Article
UDC: 
517.956
EDN: 
OJMZIH

Nonlocal Boundary-Value Problems in the Cylindrical Domain for the Multidimensional Laplace Equation

Autors: 
Aldashev Serik Aimurzaevich, Abai Kazakh National Pedagogical University
Abstract: 

Correct statements of boundary value problems on the plane for elliptic equations by the method of analytic function theory of a complex variable. Investigating similar questions, when the number of independent variablesis greater than two, problems of a fundamental nature arise. Avery attractive and convenient method of singular integral equations loses its validity due to the absence of any complete theory of multidimensional singular integral equations. The author has previously studied local boundary value problems in a cylindrical domain for multidimensional elliptic equations. As far as we know, non-local boundary-value problems for these equations have not been investigated. This paper uses the method proposed in the author’s earlier works, shows unique solvabilities, and gives explicit forms of classical solutions of nonlocal boundary-value problems in the cylindrical domain for the multidimensional Laplace equation, which are generalizations of the mixed problem, the Dirichlet and Poincare problems. A criterion for uniqueness is also obtained for regular solutions of these problems is also obtained.

References: 
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  2. Aldashev S. A. Correctness of Poincare’s problem in a cylindrical region for Laplace’s multi-measured equation. News of the National Academy of Sciences of the Republic of Kazakhstan. Physical-mathematical Series, 2014, no. 3 (295), pp. 62–67 (in Russian).
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Received: 
02.09.2017
Accepted: 
05.06.2018
Published: 
28.02.2019
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