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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 8, Pages 1351–1366 (Mi zvmmf11116)  

On boundary value problems for an improperly elliptic equation in a circle

V. P. Burskiiab, E. V. Lesinac

a Moscow Institute of Physics and Technology, Dolgoprudny, Moscow oblast, 141701 Russia
b RUDN University, Moscow, 117198 Russia
c Donetsk National Technical University, Pokrovsk, Donetsk oblast, 85300 Ukraine

Abstract: The paper considers the solvability of the first, second, and third boundary value problems, as well as one problem with a directional derivative, in a bounded domain for a scalar improperly elliptic differential equation with complex coefficients. More detailed consideration is given to a model case in which the domain is a unit disk and the equation does not contain lower-order terms. For each of these problems, the classes of boundary data for which there exists a unique solution in the ordinary Sobolev space are characterized. In a typical case, such classes turned out to be the spaces of function with exponentially decreasing Fourier coefficients. These problems have been the subject of several previous publications of the authors, and, in this article, the earlier-obtained results have been collected together and are presented from a unified point of view.

Key words: improperly elliptic equations, boundary value problems in a disk, Sobolev spaces, Dirichlet problem, Neumann problem, Poincaré problem, third boundary value problem.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 5-100
This work was supported by the Program of the RUDN University “5-100”.


DOI: https://doi.org/10.31857/S0044466920080050


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1306–1321

Bibliographic databases:

UDC: 517.95
Received: 15.02.2020
Revised: 15.02.2020
Accepted:09.04.2020

Citation: V. P. Burskii, E. V. Lesina, “On boundary value problems for an improperly elliptic equation in a circle”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1351–1366; Comput. Math. Math. Phys., 60:8 (2020), 1306–1321

Citation in format AMSBIB
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\paper On boundary value problems for an improperly elliptic equation in a circle
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 8
\pages 1351--1366
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\crossref{https://doi.org/10.31857/S0044466920080050}
\elib{https://elibrary.ru/item.asp?id=43824049}
\transl
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 8
\pages 1306--1321
\crossref{https://doi.org/10.1134/S0965542520080059}
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