The Friedrichs extension for elliptic wedge operators of second order

Thomas Krainer, Gerardo A. Mendoza

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let M be a smooth compact manifold whose boundary is the total space of a fibration N → Y with compact fibers, let E → M be a vector bundle. Let be a second order elliptic semibounded wedge operator. Under certain mild natural conditions on the indicial and normal families of A, the trace bundle of A relative to ν splits as a direct sum I = IF ⊕ IaF and there is a natural map P: C(Y;IF) → C(M; E) such that CIF (M; E) = P(C(Y;IF)) + Ċ(M;E) ⊂ Dmax(A). It is shown that the closure of A when given the domain CIF (M;E) is the Friedrichs extension of (†) and that this extension is a Fredholm operator with compact resolvent. Also given are theorems pertaining the structure of the domain of the extension which completely characterize the regularity of its elements at the boundary.

Original languageEnglish (US)
Pages (from-to)295-328
Number of pages34
JournalAdvances in Differential Equations
Volume23
Issue number3-4
StatePublished - Mar 1 2018

Fingerprint

Friedrichs Extension
Wedge
Normal Family
Fredholm Operator
Fibers
Smooth Manifold
Fibration
Operator
Resolvent
Direct Sum
Vector Bundle
Compact Manifold
Bundle
Closure
Regularity
Trace
Fiber
Theorem

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

@article{6d3767e537cd42d4ae90a693deea16e9,
title = "The Friedrichs extension for elliptic wedge operators of second order",
abstract = "Let M be a smooth compact manifold whose boundary is the total space of a fibration N → Y with compact fibers, let E → M be a vector bundle. Let be a second order elliptic semibounded wedge operator. Under certain mild natural conditions on the indicial and normal families of A, the trace bundle of A relative to ν splits as a direct sum I = IF ⊕ IaF and there is a natural map P: C∞(Y;IF) → C∞(M; E) such that CIF ∞(M; E) = P(C∞(Y;IF)) + Ċ∞(M;E) ⊂ Dmax(A). It is shown that the closure of A when given the domain CIF ∞(M;E) is the Friedrichs extension of (†) and that this extension is a Fredholm operator with compact resolvent. Also given are theorems pertaining the structure of the domain of the extension which completely characterize the regularity of its elements at the boundary.",
author = "Thomas Krainer and Mendoza, {Gerardo A.}",
year = "2018",
month = "3",
day = "1",
language = "English (US)",
volume = "23",
pages = "295--328",
journal = "Advances in Differential Equations",
issn = "1079-9389",
publisher = "Khayyam Publishing, Inc.",
number = "3-4",

}

The Friedrichs extension for elliptic wedge operators of second order. / Krainer, Thomas; Mendoza, Gerardo A.

In: Advances in Differential Equations, Vol. 23, No. 3-4, 01.03.2018, p. 295-328.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The Friedrichs extension for elliptic wedge operators of second order

AU - Krainer, Thomas

AU - Mendoza, Gerardo A.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - Let M be a smooth compact manifold whose boundary is the total space of a fibration N → Y with compact fibers, let E → M be a vector bundle. Let be a second order elliptic semibounded wedge operator. Under certain mild natural conditions on the indicial and normal families of A, the trace bundle of A relative to ν splits as a direct sum I = IF ⊕ IaF and there is a natural map P: C∞(Y;IF) → C∞(M; E) such that CIF ∞(M; E) = P(C∞(Y;IF)) + Ċ∞(M;E) ⊂ Dmax(A). It is shown that the closure of A when given the domain CIF ∞(M;E) is the Friedrichs extension of (†) and that this extension is a Fredholm operator with compact resolvent. Also given are theorems pertaining the structure of the domain of the extension which completely characterize the regularity of its elements at the boundary.

AB - Let M be a smooth compact manifold whose boundary is the total space of a fibration N → Y with compact fibers, let E → M be a vector bundle. Let be a second order elliptic semibounded wedge operator. Under certain mild natural conditions on the indicial and normal families of A, the trace bundle of A relative to ν splits as a direct sum I = IF ⊕ IaF and there is a natural map P: C∞(Y;IF) → C∞(M; E) such that CIF ∞(M; E) = P(C∞(Y;IF)) + Ċ∞(M;E) ⊂ Dmax(A). It is shown that the closure of A when given the domain CIF ∞(M;E) is the Friedrichs extension of (†) and that this extension is a Fredholm operator with compact resolvent. Also given are theorems pertaining the structure of the domain of the extension which completely characterize the regularity of its elements at the boundary.

UR - http://www.scopus.com/inward/record.url?scp=85038361267&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038361267&partnerID=8YFLogxK

M3 - Article

VL - 23

SP - 295

EP - 328

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 3-4

ER -