论文标题
Harnack不平等和主要的无限LAPLACIAN运营商的主要本质和梯度，$ \ Mathbb {r}^n $和应用程序
Harnack inequality and principal eigentheory for general infinity Laplacian operators with gradient in $\mathbb{R}^N$ and applications
论文作者
论文摘要
在缺乏变分结构和非修饰性的情况下，我们研究了\ textit {gentrization eigenvalue}的三个概念，用于具有梯度和均匀术语的一般无限拉普拉斯操作员。事实证明，哈纳克不平等和边界不平等现象可以支持我们的分析。这是我们的第一份作品[3]的延续，也是对\ textit {概括的主要特征值}的发展的贡献[8、13、12、12、9、29]。我们使用这些概念来表征最大原理的有效性，并研究整个空间中Fisher-KPP类型方程的正溶液的存在，不存在和唯一性。对于无限拉普拉斯（Infinity Laplacian）来解决问题，以本质上改进了滑动方法。结果与Liouville类型的结果有关，该结果将经过精心解释。
Under the lack of variational structure and nondegeneracy, we investigate three notions of \textit{generalized principal eigenvalue} for a general infinity Laplacian operator with gradient and homogeneous term. A Harnack inequality and boundary Harnack inequality are proved to support our analysis. This is a continuation of our first work [3] and a contribution in the development of the theory of \textit{generalized principal eigenvalue} beside the works [8, 13, 12, 9, 29]. We use these notions to characterize the validity of maximum principle and study the existence, nonexistence and uniqueness of positive solutions of Fisher-KPP type equations in the whole space. The sliding method is intrinsically improved for infinity Laplacian to solve the problem. The results are related to the Liouville type results, which will be meticulously explained.
