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

Tumalun, Nicky Kurnia

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 16 No 3 (2022): BAREKENG: Journal of Mathematics and Its Applications

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