### Elliptic equations in weighted Sobolev spaces on unbounded domains.

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In this review article we present an overview on some a priori estimates in ${L}^{p}$, $p>1$, recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two ${L}^{p}$-bounds, $p>2$, for the solution...

In this paper we obtain some results about a class of functions $\rho \phantom{\rule{0.166667em}{0ex}}:\phantom{\rule{0.166667em}{0ex}}\Omega \to {R}_{+}$, where $\Omega $ is an open set of ${R}^{n}$, which are related to the distance function from a fixed subset ${S}_{\rho}\subset \partial \Omega $. We deduce some imbedding theorems in weighted Sobolev spaces, where the weight function is a power of a function $\rho $.

In this paper an existence and uniqueness theorem for the Dirichlet problem in ${W}^{2,p}$ for second order linear elliptic equations in the plane is proved. The leading coefficients are assumed here to be of class .

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