论文标题
平面障碍的低能量散射渐进疗法
Low energy scattering asymptotics for planar obstacles
论文作者
论文摘要
我们为平面障碍物的分解计算低能量渐近学，并针对相应的散射矩阵，散射阶段和外部dirichlet到neumann操作员推断渐近学。我们使用VODEV的身份将障碍物分解与自由分辨率的分解以及Petkov和Zworski的身份将散射矩阵与分辨率相关联。主要的奇异性是根据障碍物的对数能力或罗宾常数给出的。我们希望这些结果能够保留在$ \ Mathbb r^2 $上对Laplacian进行更一般的紧凑支持的扰动，并在通用的假设中对Robin常量进行了适当修改的定义，即该频谱在零处是常规的。
We compute low energy asymptotics for the resolvent of a planar obstacle, and deduce asymptotics for the corresponding scattering matrix, scattering phase, and exterior Dirichlet-to-Neumann operator. We use an identity of Vodev to relate the obstacle resolvent to the free resolvent and an identity of Petkov and Zworski to relate the scattering matrix to the resolvent. The leading singularities are given in terms of the obstacle's logarithmic capacity or Robin constant. We expect these results to hold for more general compactly supported perturbations of the Laplacian on $\mathbb R^2$, with the definition of the Robin constant suitably modified, under a generic assumption that the spectrum is regular at zero.
