Boundary value problems for elliptic partial differential operators on bounded domains

Jussi Behrndt; M. Langer

doi:10.1016/j.jfa.2006.10.009

Boundary value problems for elliptic partial differential operators on bounded domains

Jussi Behrndt, M. Langer

Mathematics And Statistics

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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.

Original language	English
Pages (from-to)	536-565
Number of pages	30
Journal	Journal of Functional Analysis
Volume	243
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2006.10.009
Publication status	Published - 15 Feb 2007

Keywords

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

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10.1016/j.jfa.2006.10.009

Behrndt-Langer-JFA2007-Boundary-value-problems-elliptic-partial-differential-operators-bounded-domainsAccepted author manuscript, 302 KBLicence: CC BY-NC-ND 4.0

Cite this

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title = "Boundary value problems for elliptic partial differential operators on bounded domains",

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.",

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

author = "Jussi Behrndt and M. Langer",

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T1 - Boundary value problems for elliptic partial differential operators on bounded domains

AU - Behrndt, Jussi

AU - Langer, M.

PY - 2007/2/15

Y1 - 2007/2/15

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.

AB - 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.

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

U2 - 10.1016/j.jfa.2006.10.009

DO - 10.1016/j.jfa.2006.10.009

M3 - Article

SN - 0022-1236

VL - 243

SP - 536

EP - 565

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Boundary value problems for elliptic partial differential operators on bounded domains

Abstract

Keywords

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