论文标题
特征函数的几何形状的形状变化结果
A shape variation result via the geometry of eigenfunctions
论文作者
论文摘要
我们讨论了一些几何特性，例如Zaremba问题的第一个特征性问题，例如环形域上的Zaremba问题的第一个特征函数，例如轴向和阳性方向的单调性。这些精细的几何特性以及形状的微积分，有助于我们证明，随着内球向外球的边界移动，第一个特征值正在严格降低。
We discuss some of the geometric properties, such as the foliated Schwarz symmetry, the monotonicity along the axial and the affine-radial directions, of the first eigenfunctions of the Zaremba problem for the Laplace operator on annular domains. These fine geometric properties, together with the shape calculus, help us to prove that the first eigenvalue is strictly decreasing as the inner ball moves towards the boundary of the outer ball.
