无穷退化椭圆方程解的局部有界性、极大值原理与连续性
经典分析与常微分方程
2016-02-23 v5
摘要
我们为无穷退化度量开发了子表示不等式，并获得了相应的 Poincaré 和 Sobolev 不等式。然后我们推导了退化度量的条件，在这些条件下，具有粗糙系数的相关无穷退化方程的弱解是局部有界的、满足极大值原理或连续的。作为应用，我们获得了某些具有光滑系数且具有温和非线性和退化性的无穷退化拟线性方程的 W-次椭圆性。
引用
@article{arxiv.1506.09203,
title = {Local boundedness, maximum principles, and continuity of solutions to infinitely degenerate elliptic equations},
author = {Lyudmila Korobenko and Cristian Rios and Eric Sawyer and Ruipeng Shen},
journal= {arXiv preprint arXiv:1506.09203},
year = {2016}
}
备注
185 pages. Proof of Sobolev inequality fixed, changed back to the correct proof in earlier versions. The radius r on the right hand side of Sobolev inequality is replaced by a different quantity called superradius. This version is submitted for publication