Elliptic boundary problems on manifolds with polycylindrical ends

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we then deal with boundary value problems for cusp differential operators. We introduce an adapted Boutet de Monvel's calculus of pseudodifferential boundary value problems, and construct parametrices for elliptic cusp operators within this calculus. Fredholm solvability and elliptic regularity up to the boundary and up to infinity for boundary value problems on manifolds with polycylindrical ends follows.

Original languageEnglish (US)
Pages (from-to)351-386
Number of pages36
JournalJournal of Functional Analysis
Volume244
Issue number2
DOIs
StatePublished - Mar 15 2007

Fingerprint

Boundary Problem
Elliptic Problems
Boundary Value Problem
Cusp
Calculus
Elliptic Regularity
Elliptic Boundary Value Problems
Codimension
Solvability
Differential operator
Infinity
Operator

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

@article{e7ee0ff4026b4043990460e357df09e7,
title = "Elliptic boundary problems on manifolds with polycylindrical ends",
abstract = "We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we then deal with boundary value problems for cusp differential operators. We introduce an adapted Boutet de Monvel's calculus of pseudodifferential boundary value problems, and construct parametrices for elliptic cusp operators within this calculus. Fredholm solvability and elliptic regularity up to the boundary and up to infinity for boundary value problems on manifolds with polycylindrical ends follows.",
author = "Thomas Krainer",
year = "2007",
month = "3",
day = "15",
doi = "10.1016/j.jfa.2006.09.018",
language = "English (US)",
volume = "244",
pages = "351--386",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "2",

}

Elliptic boundary problems on manifolds with polycylindrical ends. / Krainer, Thomas.

In: Journal of Functional Analysis, Vol. 244, No. 2, 15.03.2007, p. 351-386.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Elliptic boundary problems on manifolds with polycylindrical ends

AU - Krainer, Thomas

PY - 2007/3/15

Y1 - 2007/3/15

N2 - We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we then deal with boundary value problems for cusp differential operators. We introduce an adapted Boutet de Monvel's calculus of pseudodifferential boundary value problems, and construct parametrices for elliptic cusp operators within this calculus. Fredholm solvability and elliptic regularity up to the boundary and up to infinity for boundary value problems on manifolds with polycylindrical ends follows.

AB - We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we then deal with boundary value problems for cusp differential operators. We introduce an adapted Boutet de Monvel's calculus of pseudodifferential boundary value problems, and construct parametrices for elliptic cusp operators within this calculus. Fredholm solvability and elliptic regularity up to the boundary and up to infinity for boundary value problems on manifolds with polycylindrical ends follows.

UR - http://www.scopus.com/inward/record.url?scp=33846839149&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846839149&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2006.09.018

DO - 10.1016/j.jfa.2006.09.018

M3 - Article

AN - SCOPUS:33846839149

VL - 244

SP - 351

EP - 386

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -