Continuity of weak solutions to rough infinitely degenerate equations
arXiv:1703.00774
Abstract
We obtain a generalization of the DeGiorgi Lemma to the infinitely degenerate regime and apply it to obtain continuity of weak solutions to certain infinitely degenerate equations. This reproduces the continuity result obtained in arXiv:1506.09203 via Moser iteration, but only for homogeneous equations. However, the proofs are much less technical and more transparent.
A section on Orlicz-Sobolev inequality added. Proof of Theorem 2 (continuity of week solutions) is slightly adjusted. arXiv admin note: text overlap with arXiv:1608.01630