论文标题
$ \ Mathbb {r}^d $ seconder eelliptic运算符的概括性特征值与粗糙的非局部内核
Generalized principal eigenvalues on $\mathbb{R}^d$ of second order elliptic operators with rough nonlocal kernels
论文作者
论文摘要
我们研究了一类无数差椭圆算子的整个空间上的广义特征值问题。非局部操作员超过有限的度量，但这没有特殊的结构。我们的一些结果甚至适用于单数内核。本文的第一部分介绍了有关主要本征函数的结果。然后，我们提出各种必要的和/或足够的条件，以使最大原理保持原则，并使用这些条件来表征主要特征值的简单性。
We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has no particular structure. Some of our results even hold for singular kernels. The first part of the paper presents results concerning the existence of a principal eigenfunction. Then we present various necessary and/or sufficient conditions for the maximum principle to hold, and use these to characterize the simplicity of the principal eigenvalue.
