On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk
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 f...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/20/4360 |
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| author | Astamur Bagapsh Alexandre Soldatov |
| author_facet | Astamur Bagapsh Alexandre Soldatov |
| author_sort | Astamur Bagapsh |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T21:05:15Z |
| format | Article |
| id | doaj.art-e813b110db9c4ddc8811b0b809042768 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:05:15Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e813b110db9c4ddc8811b0b8090427682023-11-19T17:14:54ZengMDPI AGMathematics2227-73902023-10-011120436010.3390/math11204360On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit DiskAstamur Bagapsh0Alexandre Soldatov1Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 40 Vavilova St., Moscow 119333, RussiaFederal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 40 Vavilova St., Moscow 119333, RussiaThe 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.https://www.mdpi.com/2227-7390/11/20/4360Dirichlet problemsecond-order elliptic systemintegral representationPoisson integralunit diskFredholm property |
| spellingShingle | Astamur Bagapsh Alexandre Soldatov On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk Mathematics Dirichlet problem second-order elliptic system integral representation Poisson integral unit disk Fredholm property |
| title | On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk |
| title_full | On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk |
| title_fullStr | On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk |
| title_full_unstemmed | On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk |
| title_short | On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk |
| title_sort | on the solution of the dirichlet problem for second order elliptic systems in the unit disk |
| topic | Dirichlet problem second-order elliptic system integral representation Poisson integral unit disk Fredholm property |
| url | https://www.mdpi.com/2227-7390/11/20/4360 |
| work_keys_str_mv | AT astamurbagapsh onthesolutionofthedirichletproblemforsecondorderellipticsystemsintheunitdisk AT alexandresoldatov onthesolutionofthedirichletproblemforsecondorderellipticsystemsintheunitdisk |