EQUIVALENCE OF THE FREDHOLM SOLVABILITY CONDITION FOR THE NEUMANN PROBLEM TO THE COMPLEMENTARITY CONDITION
The methods of complex analysis constitute the classical direction in the study of elliptic equations and mixed-type equations on the plane and fundamental results have now been obtained. In the early 60s of the last century, a new theoretical-functional approach was developed for elliptic equations...
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| Format: | Article |
| Language: | English |
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Al-Farabi Kazakh National University
2021-09-01
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| Series: | Вестник КазНУ. Серия математика, механика, информатика |
| Subjects: | |
| Online Access: | https://bm.kaznu.kz/index.php/kaznu/article/view/947/619 |
| _version_ | 1811176367758245888 |
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| author | B. D. Koshanov A. D. Kuntuarova |
| author_facet | B. D. Koshanov A. D. Kuntuarova |
| author_sort | B. D. Koshanov |
| collection | DOAJ |
| description | The methods of complex analysis constitute the classical direction in the study of elliptic equations and mixed-type equations on the plane and fundamental results have now been obtained. In the early 60s of the last century, a new theoretical-functional approach was developed for elliptic equations and systems based on the use of functions analytic by Douglis. In the works of A.P. Soldatov and Yeh, it turned out that in the theory of elliptic equations and systems, Douglis analytic functions play an important role. These functions are solutions of a first-order elliptic system generalizing the classical Cauchy-Riemann system. In this paper, the Fredholm solvability of the generalized Neumann problem for a high-order elliptic equation on a plane is investigated. The equivalence of the solvability condition of the generalized Neumann problem with the complementarity condition (Shapiro-Lopatinsky condition) is proved. The formula for the index of the specified problem in the class of functions under study is calculated. |
| first_indexed | 2024-04-10T19:50:18Z |
| format | Article |
| id | doaj.art-1c60b18da6af40bf8d788520eb2d1f56 |
| institution | Directory Open Access Journal |
| issn | 1563-0277 2617-4871 |
| language | English |
| last_indexed | 2024-04-10T19:50:18Z |
| publishDate | 2021-09-01 |
| publisher | Al-Farabi Kazakh National University |
| record_format | Article |
| series | Вестник КазНУ. Серия математика, механика, информатика |
| spelling | doaj.art-1c60b18da6af40bf8d788520eb2d1f562023-01-28T07:26:04ZengAl-Farabi Kazakh National UniversityВестник КазНУ. Серия математика, механика, информатика1563-02772617-48712021-09-0111133951https://doi.org/10.26577/JMMCS.2021.v111.i3.04EQUIVALENCE OF THE FREDHOLM SOLVABILITY CONDITION FOR THE NEUMANN PROBLEM TO THE COMPLEMENTARITY CONDITIONB. D. Koshanov0A. D. Kuntuarova1Kazakh national pedagogical university named after Abai, Kazakhstan, AlmatyKazakh national pedagogical university named after Abai, Kazakhstan, AlmatyThe methods of complex analysis constitute the classical direction in the study of elliptic equations and mixed-type equations on the plane and fundamental results have now been obtained. In the early 60s of the last century, a new theoretical-functional approach was developed for elliptic equations and systems based on the use of functions analytic by Douglis. In the works of A.P. Soldatov and Yeh, it turned out that in the theory of elliptic equations and systems, Douglis analytic functions play an important role. These functions are solutions of a first-order elliptic system generalizing the classical Cauchy-Riemann system. In this paper, the Fredholm solvability of the generalized Neumann problem for a high-order elliptic equation on a plane is investigated. The equivalence of the solvability condition of the generalized Neumann problem with the complementarity condition (Shapiro-Lopatinsky condition) is proved. The formula for the index of the specified problem in the class of functions under study is calculated.https://bm.kaznu.kz/index.php/kaznu/article/view/947/619higher order elliptic equationsgeneralized neumann problemfredholm solvability of the problemnormal derivatives on the boundary |
| spellingShingle | B. D. Koshanov A. D. Kuntuarova EQUIVALENCE OF THE FREDHOLM SOLVABILITY CONDITION FOR THE NEUMANN PROBLEM TO THE COMPLEMENTARITY CONDITION Вестник КазНУ. Серия математика, механика, информатика higher order elliptic equations generalized neumann problem fredholm solvability of the problem normal derivatives on the boundary |
| title | EQUIVALENCE OF THE FREDHOLM SOLVABILITY CONDITION FOR THE NEUMANN PROBLEM TO THE COMPLEMENTARITY CONDITION |
| title_full | EQUIVALENCE OF THE FREDHOLM SOLVABILITY CONDITION FOR THE NEUMANN PROBLEM TO THE COMPLEMENTARITY CONDITION |
| title_fullStr | EQUIVALENCE OF THE FREDHOLM SOLVABILITY CONDITION FOR THE NEUMANN PROBLEM TO THE COMPLEMENTARITY CONDITION |
| title_full_unstemmed | EQUIVALENCE OF THE FREDHOLM SOLVABILITY CONDITION FOR THE NEUMANN PROBLEM TO THE COMPLEMENTARITY CONDITION |
| title_short | EQUIVALENCE OF THE FREDHOLM SOLVABILITY CONDITION FOR THE NEUMANN PROBLEM TO THE COMPLEMENTARITY CONDITION |
| title_sort | equivalence of the fredholm solvability condition for the neumann problem to the complementarity condition |
| topic | higher order elliptic equations generalized neumann problem fredholm solvability of the problem normal derivatives on the boundary |
| url | https://bm.kaznu.kz/index.php/kaznu/article/view/947/619 |
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