Weak Harnack inequality
= Weak Harnack inequality
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The weak estimate for supersolutions is distinct from the sup-to-inf <Harnack inequality for uniformly elliptic divergence-form equations> for solutions.
For a nonnegative weak supersolution of a uniformly elliptic divergence-form equation, a positive $L^q$ mean on a ball is bounded by a constant times the infimum on a smaller concentric ball. The admissible exponent and constant depend only on dimension and the ellipticity bounds.