论文标题
Calderón预测家庭的连续性
Continuity of family of Calderón projections
论文作者
论文摘要
我们考虑了与边界平滑的紧凑型歧管，连续的线性椭圆差分差异家族。假设内部解决方案的空间不断尺寸，我们证明了基础椭圆算子家族的正交化calderón预测形成了连续的投影家族。因此，其图像（库奇数据空间）形成了相关Sobolev空间中封闭子空间的连续家族。我们仅使用基本工具和经典结果：对Banach空间中操作员图和其他封闭子空间的基本操作；椭圆规律；格林的公式和索波列夫空间的定理；良好的边界条件；希尔伯特空间中空间和运营商的双重性；以及Sobolev空间中操作员的插值定理。 \关键字{calder {calder {ó} n投影\和cauchy数据空间\和椭圆形差分运算符\ and green的公式\ and interpolation theorem \ and comminder \ and commaret \ and parameter依赖\ and trace trace theorem \ and variatiational proporties
We consider a continuous family of linear elliptic differential operators of arbitrary order over a smooth compact manifold with boundary. Assuming constant dimension of the spaces of inner solutions, we prove that the orthogonalized Calderón projections of the underlying family of elliptic operators form a continuous family of projections. Hence, its images (the Cauchy data spaces) form a continuous family of closed subspaces in the relevant Sobolev spaces. We use only elementary tools and classical results: basic manipulations of operator graphs and other closed subspaces in Banach spaces; elliptic regularity; Green's formula and trace theorems for Sobolev spaces; well-posed boundary conditions; duality of spaces and operators in Hilbert space; and the interpolation theorem for operators in Sobolev spaces. \keywords{Calder{ó}n projection\and Cauchy data spaces \and Elliptic differential operators \and Green's formula\and Interpolation theorem\and Manifolds with boundary\and Parameter dependence \and Trace theorem \and Variational properties
