论文标题
强大的最大原理和无限拉普拉斯的紧凑支持原理
A Strong Maximum Principle and a Compact Support Principle for infinity Laplacian
论文作者
论文摘要
在本文中，我们发现了强大的最大原理和紧凑的支持原理的必要条件，用于对Quasilinear椭圆形不等式的非负解决方案$$Δ__\ Infty U + g（| du |） - f（u）\，\ leq 0 \ leq 0 \ quad quad \ quad \ text {in} \; \ Mathcal {o}，$$和$$δ_\ infty U + g（| du |） - f（u）\，\ geq 0 \ quad \ quad \ text \ text {in} \; \ Mathcal {o}，$$其中$ \ Mathcal {o} $表示Infinity Laplacian，$ G $是一个适当的连续功能，$ f $是一个不稳定的连续功能，$ f（0）= 0 $。
In this article we find necessary and sufficient conditions for the strong maximum principle and compact support principle for non-negative solutions to the quasilinear elliptic inequalities $$Δ_\infty u + G(|Du|) - f(u)\,\leq 0\quad \text{in}\; \mathcal{O},$$ and $$Δ_\infty u + G(|Du|) - f(u)\,\geq 0\quad \text{in}\; \mathcal{O},$$ where $\mathcal{O}$ denotes the infinity Laplacian, $G$ is an appropriate continuous function and $f$ is a nondecreasing, continuous function with $f(0)=0$.
