粗糙外扰动Dirichlet谱的一致稳定性
Uniform stability of the Dirichlet spectrum for rough outer perturbations
摘要：
本文的目的是研究有界域$Ω\subset Ω'$的Dirichlet特征值.与当地的谱稳定性要求$Ω$，我们表明，$Ω'$和$Ω$的狄利克雷特征值的差异是明确控制从上面的$Ω'\setminus\barΩ$的第一特征值和几何常数取决于内域$Ω$。特别地，$Ω'$可以是任意有界域。
英文摘要：
The goal of this paper is to study the Dirichlet eigenvalues of bounded domains $Ω\subset Ω'$. With a local spectral stability requirement on $Ω$, we show that the difference of the Dirichlet eigenvalues of $Ω'$ and $Ω$ is explicitly controlled from above in terms of the first eigenvalue of $Ω'\setminus\barΩ$ and of geometric constants depending on the inner domain $Ω$. In particular, $Ω'$ can be an arbitrary bounded domain.
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