Boundary value problems for elliptic partial differential operators on bounded domains

Jussi Behrndt, M. Langer

Research output: Contribution to journalArticle

71 Citations (Scopus)

Abstract

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_Θ 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.
LanguageEnglish
Pages536-565
Number of pages30
JournalJournal of Functional Analysis
Volume243
Issue number2
DOIs
Publication statusPublished - 15 Feb 2007

Fingerprint

Partial Differential Operators
Bounded Domain
Boundary Value Problem
Deficiency Index
Self-adjoint Extension
Symmetric Operator
Elliptic Problems
Hilbert space
Restriction
Eigenvalue
Boundary conditions
Dependent
Operator
Framework
Class
Concepts

Keywords

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

Cite this

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Boundary value problems for elliptic partial differential operators on bounded domains. / Behrndt, Jussi; Langer, M.

In: Journal of Functional Analysis, Vol. 243, No. 2, 15.02.2007, p. 536-565.

Research output: Contribution to journalArticle

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AU - Langer, M.

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N2 - 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_Θ 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.

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KW - boundary triple

KW - self-adjoint extension

KW - weyl function

KW - M-operator

KW - Dirichlet-to-Neumann map

KW - Krein's formula

KW - elliptic differential operator

KW - boundary value problem

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JO - Journal of Functional Analysis

T2 - Journal of Functional Analysis

JF - Journal of Functional Analysis

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