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 existence and uniqueness of this Dirichlet problem by directly using the Lax-Milgram Lemma and the weighted estimation in Morrey spaces

Abstract licence: CC BY-SA

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