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We obtain local boundedness and maximum principles for weak subsolutions tocertain infinitely degenerate elliptic divergence form equations, and the localboundedness turns out to be sharp in more than two dimensions, answering the`Moser gap' problem left open in arXiv:1506.09203v5. Finally we obtain amaximum principle for weak solutions under the same condition on thedegeneracy.

Sharp local boundedness and maximum principle in the infinitely degenerate regime via DeGiorgi iteration