Boundary value problems for elliptic partial differential operators on bounded domains

被引：97

作者：

Behrndt, Jussi

Langer, Matthias

机构：

[1] Univ Strathclyde, Dept Math, Glasgow G1 1XH, Lanark, Scotland

[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2007年 / 243卷 / 02期

关键词：

boundary triple; self-adjoint extension; Weyl function; M-operator; Dirichlet-to-Neumann map; Krein's formula; elliptic differential operator; boundary value problem;

D O I：

10.1016/j.jfa.2006.10.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a symmetric operator or relation A with infinite deficiency indices in a Hilbert space we develop an abstract framework for the description of symmetric and self-adjoint extensions A(Theta) of A as restrictions of an operator or relation T which is a core of the adjoint A*. This concept is applied to second order elliptic partial differential operators on smooth bounded domains, and a class of elliptic problems with eigenvalue dependent boundary conditions is investigated. (C) 2006 Elsevier Inc. All rights reserved.

引用

页码：536 / 565

页数：30

共 37 条

[1]

Adams R, 1978, Sobolev spaces

[2] M operators:: a generalisation of Weyl-Titchmarsh theory [J].