最小几何假设下线性化 Monge-Ampère 方程解的 Harnack 不等式
偏微分方程分析
2012-03-19 v2 经典分析与常微分方程
摘要
我们证明了方程 L_A u = 0 的解的 Harnack 不等式，其中椭圆矩阵 A 适应于满足最小几何条件的凸函数。文中还包含了 Sobolev 不等式的一个应用。
引用
@article{arxiv.1110.5263,
title = {Harnack's inequality for solutions to the linearized Monge-Ampere equation under minimal geometric assumptions},
author = {Diego Maldonado},
journal= {arXiv preprint arXiv:1110.5263},
year = {2012}
}
备注
A claim after equation (2.12) is unsubstantiated. I'm withdrawing the manuscript until I figure out if I can fix it. The main application to Sobolev inequalities should still hold true. I thank Truyen Van Nguyen for pointing out this error