Bounded imaginary powers of differential operators on manifolds with conical singularities

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • S. Coriasco
  • E. Schrohe
  • J. Seiler

Externe Organisationen

  • Università di Torino
  • Universität Potsdam
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)235-269
Seitenumfang35
FachzeitschriftMathematische Zeitschrift
Jahrgang244
Ausgabenummer2
PublikationsstatusVeröffentlicht - Juni 2003
Extern publiziertJa

Abstract

We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B, 1 < p < ∞. Under suitable ellipticity assumptions we can define a family of complex powers Az, z ∈ ℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.

ASJC Scopus Sachgebiete

Zitieren

Bounded imaginary powers of differential operators on manifolds with conical singularities. / Coriasco, S.; Schrohe, E.; Seiler, J.
in: Mathematische Zeitschrift, Jahrgang 244, Nr. 2, 06.2003, S. 235-269.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Coriasco S, Schrohe E, Seiler J. Bounded imaginary powers of differential operators on manifolds with conical singularities. Mathematische Zeitschrift. 2003 Jun;244(2):235-269. doi: 10.1007/s00209-003-0495-1
Coriasco, S. ; Schrohe, E. ; Seiler, J. / Bounded imaginary powers of differential operators on manifolds with conical singularities. in: Mathematische Zeitschrift. 2003 ; Jahrgang 244, Nr. 2. S. 235-269.
Download
@article{dda864248cc8470895e3634d069c2e57,
title = "Bounded imaginary powers of differential operators on manifolds with conical singularities",
abstract = "We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B, 1 < p < ∞. Under suitable ellipticity assumptions we can define a family of complex powers Az, z ∈ ℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.",
author = "S. Coriasco and E. Schrohe and J. Seiler",
note = "Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",
year = "2003",
month = jun,
doi = "10.1007/s00209-003-0495-1",
language = "English",
volume = "244",
pages = "235--269",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer New York",
number = "2",

}

Download

TY - JOUR

T1 - Bounded imaginary powers of differential operators on manifolds with conical singularities

AU - Coriasco, S.

AU - Schrohe, E.

AU - Seiler, J.

N1 - Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2003/6

Y1 - 2003/6

N2 - We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B, 1 < p < ∞. Under suitable ellipticity assumptions we can define a family of complex powers Az, z ∈ ℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.

AB - We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B, 1 < p < ∞. Under suitable ellipticity assumptions we can define a family of complex powers Az, z ∈ ℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.

UR - http://www.scopus.com/inward/record.url?scp=0037633509&partnerID=8YFLogxK

U2 - 10.1007/s00209-003-0495-1

DO - 10.1007/s00209-003-0495-1

M3 - Article

AN - SCOPUS:0037633509

VL - 244

SP - 235

EP - 269

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 2

ER -