Abstract
We develop regularity theory, including a posteriori Harnack inequality and higher integrability of the gradient of solutions, for divergence-form elliptic equations with singular divergence-free drift satisfying a broad form-boundedness-type condition (more generally, our drifts can have singular divergence). A key step in our proofs is a new iteration procedure (needed already to prove Caccioppoli's inequality), which is used in addition to the classical De Giorgi's iterations and Moser's method.
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