论文标题
在哑铃域上的steklov问题的渐近行为
Asymptotic behaviour of the Steklov problem on dumbbell domains
论文作者
论文摘要
我们分析了由两个Lipschitz套件组成的哑铃结构域中特征值和特征向量的渐近行为，这些dipschitz套件由两个薄管连接，这些lipschitz套件由带有消失宽度的细管连接。所有特征值都崩溃为零，速度是由宽度的某些宽度驱动的，该宽度乘以一个维度问题的特征值。在空间的两个维度中，行为与第三或更高维度根本不同，而极限问题具有不同的性质。这种现象是由于一个事实，即仅在尺寸二下，管子的边界没有消失表面度量。
We analyse the asymptotic behaviour of the eigenvalues and eigenvectors of a Steklov problem in a dumbbell domain consisting of two Lipschitz sets connected by a thin tube with vanishing width. All the eigenvalues are collapsing to zero, the speed being driven by some power of the width which multiplies the eigenvalues of a one dimensional problem. In two dimensions of the space, the behaviour is fundamentally different from the third or higher dimensions and the limit problems are of different nature. This phenomenon is due to the fact that only in dimension two the boundary of the tube has not vanishing surface measure.
