Dirichlet to Neumann operator on differential forms

被引：36

作者：

Belishev, Mikhail ^{[2
]}

Sharafutdinov, Vladimir ^{[1
]}

机构：

[1] Sobolev Inst Math, Novosibirsk 630090, Russia

[2] VA Steklov Math Inst, Petersburg Dept, St Petersburg 191023, Russia

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2008年 / 132卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

D O I：

10.1016/j.bulsci.2006.11.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define the Dirichlet to Neumann operator on exterior differential forms for a compact Riemannian manifold with boundary and prove that the real additive cohomology structure of the manifold is determined by the DN operator. In particular, an explicit formula is obtained which expresses Betti numbers of the manifold through the DN operator. We express also the Hilbert transform through the DN map. The Hilbert transform connects boundary traces of conjugate co-closed forms. (c) 2006 Elsevier Masson SAS. All rights reserved.

引用

页码：128 / 145

页数：18

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