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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Universitas Pattimura
2022-09-01
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| Series: | Barekeng |
| Subjects: | |
| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/5508 |
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| Summary: | 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 |
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| ISSN: | 1978-7227 2615-3017 |