= Local boundedness of weak elliptic subsolutions
For a <uniformly elliptic> <divergence-form elliptic operator> with lower-order coefficients in the supercritical <Lebesgue spaces>, truncation tests and <Moser iteration> bound the <positive part> of a <weak subsolution> on an interior ball by its <Lp norm> on a larger ball and the forcing norms. In particular, every <weak subsolution> of the homogeneous equation is locally bounded above. This is the preliminary estimate needed when a <strong maximum principle> is phrased using <essential suprema>.
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