AN EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION OF THE DIRICHLET PROBLEM WITH THE DATA IN MORREY SPACES
Let n-2<\lambda<n , f be a function in Morrey spaces L^{1,\lambda}(\Omega) , and the equation Lu=f u \in W^{1,2}(\Omega) be a Dirichlet problem, where \Omega is a bounded open subset of R^{n} , n \ge 3 , L and is a divergent elliptic operator. In this paper, we prove the existe...
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Universitas Pattimura
2022-09-01
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/5508 |
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| author | Nicky Kurnia Tumalun |
| author_facet | Nicky Kurnia Tumalun |
| author_sort | Nicky Kurnia Tumalun |
| collection | DOAJ |
| description | Let n-2<\lambda<n , f be a function in Morrey spaces L^{1,\lambda}(\Omega) , and the equation
Lu=f
u \in W^{1,2}(\Omega)
be a Dirichlet problem, where \Omega is a bounded open subset of R^{n} , n \ge 3 , L and is a divergent elliptic operator. In this paper, we prove the existence and uniqueness of this Dirichlet problem by directly using the Lax-Milgram Lemma and the weighted estimation in Morrey spaces |
| format | Article |
| id | doaj-art-4dfac3cf01aa43c897cd423eb3fb895a |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2022-09-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-4dfac3cf01aa43c897cd423eb3fb895a2025-08-20T04:01:48ZengUniversitas PattimuraBarekeng1978-72272615-30172022-09-0116382983410.30598/barekengvol16iss3pp829-8345508AN EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION OF THE DIRICHLET PROBLEM WITH THE DATA IN MORREY SPACESNicky Kurnia Tumalun0Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri ManadoLet n-2<\lambda<n , f be a function in Morrey spaces L^{1,\lambda}(\Omega) , and the equation Lu=f u \in W^{1,2}(\Omega) be a Dirichlet problem, where \Omega is a bounded open subset of R^{n} , n \ge 3 , L and is a divergent elliptic operator. In this paper, we prove the existence and uniqueness of this Dirichlet problem by directly using the Lax-Milgram Lemma and the weighted estimation in Morrey spaceshttps://ojs3.unpatti.ac.id/index.php/barekeng/article/view/5508morrey spacesdirichlet problemelliptic equations |
| spellingShingle | Nicky Kurnia Tumalun AN EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION OF THE DIRICHLET PROBLEM WITH THE DATA IN MORREY SPACES Barekeng morrey spaces dirichlet problem elliptic equations |
| title | AN EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION OF THE DIRICHLET PROBLEM WITH THE DATA IN MORREY SPACES |
| title_full | AN EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION OF THE DIRICHLET PROBLEM WITH THE DATA IN MORREY SPACES |
| title_fullStr | AN EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION OF THE DIRICHLET PROBLEM WITH THE DATA IN MORREY SPACES |
| title_full_unstemmed | AN EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION OF THE DIRICHLET PROBLEM WITH THE DATA IN MORREY SPACES |
| title_short | AN EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION OF THE DIRICHLET PROBLEM WITH THE DATA IN MORREY SPACES |
| title_sort | existence and uniqueness of the weak solution of the dirichlet problem with the data in morrey spaces |
| topic | morrey spaces dirichlet problem elliptic equations |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/5508 |
| work_keys_str_mv | AT nickykurniatumalun anexistenceanduniquenessoftheweaksolutionofthedirichletproblemwiththedatainmorreyspaces AT nickykurniatumalun existenceanduniquenessoftheweaksolutionofthedirichletproblemwiththedatainmorreyspaces |