On some analogues of periodic problems for Laplace equation with an oblique derivative under boundary conditions
In this paper, we study solvability of new classes of nonlocal boundary value problems for the Laplace equation in a ball. The considered problems are multidimensional analogues (in the case of a ball) of classical periodic boundary value problems in rectangular regions. To study the main problem, f...
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| Language: | English |
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EJAAM
2020-06-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
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| Online Access: | https://ejaam.org/articles/2020/10.2478-ejaam-2020-0002.pdf |
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| author | Batirkhan Turmetov Maira Koshanova Moldir Muratbekova |
| author_facet | Batirkhan Turmetov Maira Koshanova Moldir Muratbekova |
| author_sort | Batirkhan Turmetov |
| collection | DOAJ |
| description | In this paper, we study solvability of new classes of nonlocal boundary value problems for the Laplace equation in a ball. The considered problems are multidimensional analogues (in the case of a ball) of classical periodic boundary value problems in rectangular regions. To study the main problem, first, for the Laplace equation, we consider an auxiliary boundary value problem with an oblique derivative. This problem generalizes the well-known Neumann problem and is conditionally solvable. The main problems are solved by reducing them to sequential solution of the Dirichlet problem and the problem with an oblique derivative. It is proved that in the case of periodic conditions, the problem is conditionally solvable; and in this case the exact condition for solvability of the considered problem is found. When boundary conditions are specified in the antiperiodic conditions form, the problem is certainly solvable. The obtained general results are illustrated with specific examples. |
| format | Article |
| id | doaj-art-9a27953c78244c88aad42b7ecd257f75 |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2020-06-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-9a27953c78244c88aad42b7ecd257f752025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902020-06-01202010.2478/ejaam-2020-0002On some analogues of periodic problems for Laplace equation with an oblique derivative under boundary conditionsBatirkhan Turmetov0Maira Koshanova1Moldir Muratbekova2Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, 161200, Turkistan, KazakhstanDepartment of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, 161200, Turkistan, KazakhstanDepartment of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, 161200, Turkistan, KazakhstanIn this paper, we study solvability of new classes of nonlocal boundary value problems for the Laplace equation in a ball. The considered problems are multidimensional analogues (in the case of a ball) of classical periodic boundary value problems in rectangular regions. To study the main problem, first, for the Laplace equation, we consider an auxiliary boundary value problem with an oblique derivative. This problem generalizes the well-known Neumann problem and is conditionally solvable. The main problems are solved by reducing them to sequential solution of the Dirichlet problem and the problem with an oblique derivative. It is proved that in the case of periodic conditions, the problem is conditionally solvable; and in this case the exact condition for solvability of the considered problem is found. When boundary conditions are specified in the antiperiodic conditions form, the problem is certainly solvable. The obtained general results are illustrated with specific examples.https://ejaam.org/articles/2020/10.2478-ejaam-2020-0002.pdfboundary value problemslaplace equationoblique derivativeperiodic conditionsuniqueness of solutionexistence of a solution |
| spellingShingle | Batirkhan Turmetov Maira Koshanova Moldir Muratbekova On some analogues of periodic problems for Laplace equation with an oblique derivative under boundary conditions E-Journal of Analysis and Applied Mathematics boundary value problems laplace equation oblique derivative periodic conditions uniqueness of solution existence of a solution |
| title | On some analogues of periodic problems for Laplace equation with an oblique derivative under boundary conditions |
| title_full | On some analogues of periodic problems for Laplace equation with an oblique derivative under boundary conditions |
| title_fullStr | On some analogues of periodic problems for Laplace equation with an oblique derivative under boundary conditions |
| title_full_unstemmed | On some analogues of periodic problems for Laplace equation with an oblique derivative under boundary conditions |
| title_short | On some analogues of periodic problems for Laplace equation with an oblique derivative under boundary conditions |
| title_sort | on some analogues of periodic problems for laplace equation with an oblique derivative under boundary conditions |
| topic | boundary value problems laplace equation oblique derivative periodic conditions uniqueness of solution existence of a solution |
| url | https://ejaam.org/articles/2020/10.2478-ejaam-2020-0002.pdf |
| work_keys_str_mv | AT batirkhanturmetov onsomeanaloguesofperiodicproblemsforlaplaceequationwithanobliquederivativeunderboundaryconditions AT mairakoshanova onsomeanaloguesofperiodicproblemsforlaplaceequationwithanobliquederivativeunderboundaryconditions AT moldirmuratbekova onsomeanaloguesofperiodicproblemsforlaplaceequationwithanobliquederivativeunderboundaryconditions |