论文标题
$卷发$操作员的光谱稳定性通过均匀的gaffney不平等现象
Spectral stability of the $curl curl$ operator via uniform Gaffney inequalities on perturbed electromagnetic cavities
论文作者
论文摘要
我们证明了$ curl curl $运算符的光谱稳定性结果，但在边界扰动时在腔内受到电气边界条件。假定腔体足够光滑，但我们对扰动的强度施加了弱限制。这些方法是变异类型的，基于两种主要成分：在域之间构建合适的piola型转换和通过均匀的先验$ h^2 $估计dirichlet laplacian的Poisson问题获得的均匀Gaffney不平等的证明。通过使用基于Sobolev乘数的V. maz'ya和T. shaposhnikova的结果证明了统一的先验估计值。还指出了与边界均质化问题的连接。
We prove spectral stability results for the $curl curl$ operator subject to electric boundary conditions on a cavity upon boundary perturbations. The cavities are assumed to be sufficiently smooth but we impose weak restrictions on the strength of the perturbations. The methods are of variational type and are based on two main ingredients: the construction of suitable Piola-type transformations between domains and the proof of uniform Gaffney inequalities obtained by means of uniform a priori $H^2$-estimates for the Poisson problem of the Dirichlet Laplacian. The uniform a priori estimates are proved by using the results of V. Maz'ya and T. Shaposhnikova based on Sobolev multipliers. Connections to boundary homogenization problems are also indicated.
