First-order operators and boundary triples
First-order operators and boundary triples
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一阶算子和边界三元组
DOI：
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发表时间：
2007
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通讯作者：
O. Post
中科院分区：
文献类型：
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作者：
O. Post
本文的目的是引入一种一阶方法来处理拉普拉斯算子的抽象边界三元组概念。我们的主要应用是具有边界的流形上的拉普拉斯算子；在这种情况下，普通的边界三元组的概念不直接适用。在我们的一阶方法中，我们证明了我们也可以在抽象的格林公式中使用通常的边界算子。一阶方法的另一个动机是给出Dirichlet-to-Neumann映射的内在定义和相应边界空间上的内在范数。我们还展示了如何使用一阶边界三元组来定义导致狄拉克算子的通常的边界三元组。
The aim of the present paper is to introduce a first-order approach to the abstract concept of boundary triples for Laplace operators. Our main application is the Laplace operator on a manifold with boundary; a case in which the ordinary concept of boundary triples does not apply directly. In our first-order approach, we show that we can use the usual boundary operators in abstract Green’s formula as well. Another motivation for the first-order approach is to give an intrinsic definition of the Dirichlet-to-Neumann map and intrinsic norms on the corresponding boundary spaces. We also show how the first-order boundary triples can be used to define a usual boundary triple leading to a Dirac operator.