基于DeGiorgi迭代的无穷退化区域中的尖锐局部有界性与极大值原理
经典分析与常微分方程
2019-12-16 v4
摘要
我们针对某些无穷退化椭圆散度型方程的弱下解，获得了局部有界性和极大值原理，并且该局部有界性在二维以上被证明是尖锐的，从而回答了arXiv:1506.09203v5中遗留的“Moser间隙”问题。最后，我们在相同的退化条件下得到了弱解的极大值原理。
引用
@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}
}
备注
Two errors fixed: one in the proof of the local boundedness result, and one in the proof of the maximum principle