 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.