English

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

Classical Analysis and ODEs 2019-12-16 v4

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 the same condition on the degeneracy.

Keywords

Cite

@article{arxiv.1608.01630,
  title  = {Sharp local boundedness and maximum principle in the infinitely degenerate regime via DeGiorgi iteration},
  author = {Lyudmila Korobenko and Cristian Rios and Eric Sawyer and Ruipeng Shen},
  journal= {arXiv preprint arXiv:1608.01630},
  year   = {2019}
}

Comments

Two errors fixed: one in the proof of the local boundedness result, and one in the proof of the maximum principle