Differential operators and boundary value problems on hypersurfaces

被引：39

作者：

Duduchava, L. Roland

Mitrea, Dorina

Mitrea, Marius

机构：

[1] Georgian Acad Sci, A Razmadze Math Inst, GE-93 Tbilisi, Georgia

[2] Univ Missouri, Dept Math, Columbia, MO 65211 USA

来源：

MATHEMATISCHE NACHRICHTEN | 2006年 / 279卷 / 9-10期

关键词：

tangential differential operator; hypersurface; Gunter derivative; Stokes derivative; Laplace-Beltrami operator; Lame operator; Navier-Stokes operator; Bochner-Laplacian; Hodge-Laplacian;

D O I：

10.1002/mana.200410407

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We explore the extent to which basic differential operators (such as Laplace-Beltrami, Lame, Navier-Stokes, etc.) and boundary value problems on a hypersurface S in R-n can be expressed globally, in terms of the standard spatial coordinates in R-n. The approach we develop also provides, in some important cases, useful simplifications as well as new interpretations of classical operators and equations. (C) 2006 WILEYNCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：996 / 1023

页数：28

共 36 条

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[34] Asymptotics of eigenvalues of the two-dimensional Dirichlet boundary-value problem for the Lam, operator in a domain with a small hole
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[35] Closure of the Laplace-Beltrami Operator on 2D Almost-Riemannian Manifolds and Semi-Fredholm Properties of Differential Operators on Lie Manifolds
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