On the Solvability of the Dirichlet Problem for a Multidimensional Elliptic System in the Half-Space
The Dirichlet problem for a multidimensional elliptic system in the half-space is considered. With the help of the Fourier transform, the problem of the solvability of the problem is reduced to the study of a second-order partial differential equation.
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| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 279; no. 5; pp. 635 - 643 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
23.03.2024
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1072-3374 1573-8795 |
| DOI | 10.1007/s10958-024-07044-w |
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| Abstract | The Dirichlet problem for a multidimensional elliptic system in the half-space is considered. With the help of the Fourier transform, the problem of the solvability of the problem is reduced to the study of a second-order partial differential equation. |
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| AbstractList | The Dirichlet problem for a multidimensional elliptic system in the half-space is considered. With the help of the Fourier transform, the problem of the solvability of the problem is reduced to the study of a second-order partial differential equation. The Dirichlet problem for a multidimensional elliptic system in the half-space is considered. With the help of the Fourier transform, the problem of the solvability of the problem is reduced to the study of a second-order partial differential equation. Keywords and phrases: multidimensional elliptic system, half-space, Dirichlet problem, Fourier transform, Bessel function. AMS Subject Classification: 35J57 |
| Audience | Academic |
| Author | Golovko, E. A. |
| Author_xml | – sequence: 1 givenname: E. A. surname: Golovko fullname: Golovko, E. A. email: elena-golovko@mail.ru organization: Irkutsk State University |
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| Copyright | Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. COPYRIGHT 2024 Springer |
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| Keywords | Bessel function multidimensional elliptic system Dirichlet problem Fourier transform half-space 35J57 |
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| References | VishikMIOn strongly elliptic systems of differential equationsMat. Sb.195129361567649440 A. I. Yanushauskas, Boundary-Value Problems for Partial Differential Equations and Integro-Differential Equations [in Russian], Irkutsk (1997). YanushauskasAIProblems on the Potential Theory with Slanted Derivatives1985NovosibirskNauka[in Russian] BitsadzeAVSome Classes of Partial Differential Equations1981MoscowNauka[in Russian] R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. II: Partial Differential Equations, Wiley, New York. AV Bitsadze (7044_CR1) 1981 MI Vishik (7044_CR3) 1951; 29 AI Yanushauskas (7044_CR5) 1985 7044_CR2 7044_CR4 |
| References_xml | – reference: R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. II: Partial Differential Equations, Wiley, New York. – reference: VishikMIOn strongly elliptic systems of differential equationsMat. Sb.195129361567649440 – reference: A. I. Yanushauskas, Boundary-Value Problems for Partial Differential Equations and Integro-Differential Equations [in Russian], Irkutsk (1997). – reference: BitsadzeAVSome Classes of Partial Differential Equations1981MoscowNauka[in Russian] – reference: YanushauskasAIProblems on the Potential Theory with Slanted Derivatives1985NovosibirskNauka[in Russian] – ident: 7044_CR4 – volume: 29 start-page: 615 issue: 3 year: 1951 ident: 7044_CR3 publication-title: Mat. Sb. – volume-title: Some Classes of Partial Differential Equations year: 1981 ident: 7044_CR1 – volume-title: Problems on the Potential Theory with Slanted Derivatives year: 1985 ident: 7044_CR5 – ident: 7044_CR2 |
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| SubjectTerms | Differential equations Dirichlet problem Fourier transforms Half spaces Mathematics Mathematics and Statistics Partial differential equations |
| Title | On the Solvability of the Dirichlet Problem for a Multidimensional Elliptic System in the Half-Space |
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