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Vol 16 No 3 (2022): BAREKENG: Journal of Mathematics and Its Applications
Articles

AN EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION OF THE DIRICHLET PROBLEM WITH THE DATA IN MORREY SPACES

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  • Nicky Kurnia Tumalun
Nicky Kurnia Tumalun
Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Manado
DOI: https://doi.org/10.30598/barekengvol16iss3pp829-834
Published September 1, 2022
Keywords
  • Morrey spaces,
  • Dirichlet problem,
  • elliptic equations
How to Cite
[1]
N. Tumalun, “AN EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION OF THE DIRICHLET PROBLEM WITH THE DATA IN MORREY SPACES”, BAREKENG: J. Math. & App., vol. 16, no. 3, pp. 829-834, Sep. 2022.

Copyright (c) 2022 Nicky Kurnia Tumalun

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Abstract

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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