论文标题
关于拉普拉斯操作员本征函数的本地化
On localisation of eigenfunctions of the Laplace operator
论文作者
论文摘要
我们证明了（i）一个简单的几何条件，以定位一系列dirichlet eigenfunctions的序列，前提是相应的dirichlet laplacians满足了统一的耐磨不平等，并且（ii）将一系列dirichlet eigenlet序列定位，以换取广泛的伸长角类别的角色符号。我们提供了简单连接的，平面，多边形结构域的序列的示例，为此，与dirichlet或neumann，边界条件$κ$ localise in $ l^2 $中的第一个特征函数的相应序列。
We prove (i) a simple sufficient geometric condition for localisation of a sequence of first Dirichlet eigenfunctions provided the corresponding Dirichlet Laplacians satisfy a uniform Hardy inequality, and (ii) localisation of a sequence of first Dirichlet eigenfunctions for a wide class of elongating horn-shaped domains. We give examples of sequences of simply connected, planar, polygonal domains for which the corresponding sequence of first eigenfunctions with either Dirichlet, or Neumann, boundary conditions $κ$-localise in $L^2$.
