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An existence result for elliptic equations with \(VMO\)-coefficients. (English) Zbl 1152.35025
The paper deals with existence and uniqueness of solutions to the Dirichlet problem \[ \begin{cases} u\in W^{2,p}(\Omega)\cap W^{1,p}_0(\Omega),\cr Lu=f\in L^p(\Omega), \end{cases} \] with unbounded domain \(\Omega\subset \mathbb R^n,\) \(n\geq3,\) for the linear uniformly elliptic operator \[ L=-\sum_{i,j=1}^n a_{ij}{{\partial^2}\over{\partial x_i \partial x_j}}+ \sum_{i=1}^n a_{i}{{\partial^2}\over{\partial x_i}}+a \] with \(VMO_{\text{loc}}(\Omega)\) principal coefficients.

MSC:
35J25 Boundary value problems for second-order elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
35B45 A priori estimates in context of PDEs
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