Abstract
Lorentz and Lorentz–Morrey estimates are obtained for gradients of very weak solutions to quasilinear equations of the form $$\begin{aligned} \text {div}\,\mathcal {A}(x, \nabla u)=\text {div}\, |\mathbf{f}|^{p-2}\mathbf{f}, \end{aligned}$$ where $$\text {div}\,\mathcal {A}(x, \nabla u)$$ is modelled after the p-Laplacian, $$p>1$$ . The estimates are global over bounded domains that satisfy a mild exterior uniform thickness condition that involves the p-capacity. The vector field datum $$\mathbf{f}$$ is allowed to have low degrees of integrability and thus solutions may not have finite $$L^p$$ energy. A higher integrability result at the boundary of the ground domain is also obtained for infinite energy solutions to the associated homogeneous equations.
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