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| We discuss several a priori estimates and the existence of very weak solutions, i.e., solutions with possibly infinite energy, to equations whose prototype is given by $\Delta_p u= {\rm div} |F|^{p-2}F$. Here $\Delta_p u={\rm div} |\nabla u|^{p-2}\nabla u$ is the $p$-Laplacian, $p>1$. The results are global and are obtained over domains whose complements are uniformly thick with respect to the $p$-capacity. As an application, a characterization of existence in the framework of Morrey spaces is obtained for a class of quasilinear Riccati type equations. This talk is based on joint work with Karthik Adimurthi. |
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