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