论文标题
弗里德兰式估算stokes操作员的估计
A Friedlander type estimate for Stokes operators
论文作者
论文摘要
令$ω\ subset \ mathbb {r}^d $为带有Lipschitz边界的有界开放连接集。令$ a^n $和$ a^d $分别为$ω$的Neumann Stokes Operator和Dirichlet Stokes Operator。再让$λ_1^n \leqλ_2^n \ leq \ ldots $和$λ_1^d \leqλ_2^d \ leq \ ldots $是$ a^n $和$ a^d $的eigenvalues，分别用多重性重复。然后\ [λ_{n+1}^n <λ_n^d \] in \ mathbb {n} $中的所有$ n \。
Let $Ω\subset \mathbb{R}^d$ be a bounded open connected set with Lipschitz boundary. Let $A^N$ and $A^D$ be the Neumann Stokes operator and Dirichlet Stokes operator on $Ω$, respectively. Further let $λ_1^N \leq λ_2^N \leq \ldots$ and $λ_1^D \leq λ_2^D \leq \ldots$ be the eigenvalues of $A^N$ and $A^D$ repeated with multiplicity, respectively. Then \[ λ_{n+1}^N < λ_n^D \] for all $n \in \mathbb{N}$.
