非局部Robin Laplacian算子及对Filonov关于eigenvalue不等式的一点注记
Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities
摘要：
本文的目的是双重的：首先，我们刻画了一类本质上最优的边界算子$Θ$，它在有界Lipschitz域$Ω\subset\bbR^n$，$n\in\bbN$，$n\geq 2$上产生了具有（非局部和局部）Robin型边界条件的$L^2(Ω; d^n x)$中的自伴Laplacian $-Δ_{Θ, Ω}$。其次，我们扩展Friedlander的Neumann和Dirichlet Laplacian特征值之间的非局部罗宾和Dirichlet Laplacian特征值与有界Lipschitz域$Ω$，Filonov介绍了这种类型的问题的方法。
英文摘要：
The aim of this paper is twofold: First, we characterize an essentially optimal class of boundary operators $Θ$ which give rise to self-adjoint Laplacians $-Δ_{Θ, Ω}$ in $L^2(Ω; d^n x)$ with (nonlocal and local) Robin-type boundary conditions on bounded Lipschitz domains $Ω\subset\bbR^n$, $n\in\bbN$, $n\geq 2$. Second, we extend Friedlander's inequalities between Neumann and Dirichlet Laplacian eigenvalues to those between nonlocal Robin and Dirichlet Laplacian eigenvalues associated with bounded Lipschitz domains $Ω$, following an approach introduced by Filonov for this type of problems.
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