Sharp local boundedness and maximum principle in the infinitely degenerate regime via DeGiorgi iteration Academic Article uri icon

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abstract

  • We obtain local boundedness and maximum principles for weak subsolutions to certain infinitely degenerate elliptic divergence form equations, and the local boundedness turns out to be sharp in more than two dimensions, answering the `Moser gap' problem left open in arXiv:1506.09203v5. Finally we obtain a maximum principle for weak solutions under a very mild condition on the degeneracy function f (x), essentially that -ln f (x) is merely doubling on (0;1).

authors

  • Korobenko, Lyudmila
  • Rios, Cristian
  • Sawyer, Eric
  • Shen, Ruipeng