粗糙无穷退化方程弱解的连续性
偏微分方程分析
2019-12-17 v3
摘要
我们获得了 DeGiorgi 引理向无穷退化情形的推广，并将其应用于获得某些无穷退化方程弱解的连续性。这再现了 arXiv:1506.09203 中通过 Moser 迭代获得的连续性结果，但仅适用于齐次方程。然而，其证明的技术性大大降低且更为透明。
引用
@article{arxiv.1703.00774,
title = {Continuity of weak solutions to rough infinitely degenerate equations},
author = {Lyudmila Korobenko and Cristian Rios and Eric Sawyer and Ruipeng Shen},
journal= {arXiv preprint arXiv:1703.00774},
year = {2019}
}
备注
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