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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
##### Keywords:
linear elliptic equations; $$VMO$$-coefficients
Full Text:
##### References:
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