Resolvent estimates for elliptic systems in function spaces of higher regularity

Robert Denk, Michael Dreher

Research output: Contribution to journalArticle

Abstract

We consider parameter-elliptic boundary value problems and uniform a priori estimates in L-p-Sobolev spaces of Bessel potential and Besov type. The problems considered are systems of uniform order and mixed-order systems (Douglis-Nirenberg systems). It is shown that compatibility conditions on the data are necessary for such estimates to hold. In particular, we consider the realization of the boundary value problem as an unbounded operator with the ground space being a closed subspace of a Sobolev space and give necessary and sufficient conditions for the realization to generate an analytic semigroup.

Original languageEnglish
Article number109
Number of pages12
JournalElectronic Journal of Differential Equations
Volume2011
Publication statusPublished - 2011

Keywords

  • Parameter-ellipticity
  • Douglis-Nirenberg systems
  • analytic semigroups
  • BOUNDARY-VALUE-PROBLEMS
  • EIGENVALUE ASYMPTOTICS
  • EQUATIONS

Cite this

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title = "Resolvent estimates for elliptic systems in function spaces of higher regularity",
abstract = "We consider parameter-elliptic boundary value problems and uniform a priori estimates in L-p-Sobolev spaces of Bessel potential and Besov type. The problems considered are systems of uniform order and mixed-order systems (Douglis-Nirenberg systems). It is shown that compatibility conditions on the data are necessary for such estimates to hold. In particular, we consider the realization of the boundary value problem as an unbounded operator with the ground space being a closed subspace of a Sobolev space and give necessary and sufficient conditions for the realization to generate an analytic semigroup.",
keywords = "Parameter-ellipticity, Douglis-Nirenberg systems, analytic semigroups, BOUNDARY-VALUE-PROBLEMS, EIGENVALUE ASYMPTOTICS, EQUATIONS",
author = "Robert Denk and Michael Dreher",
year = "2011",
language = "English",
volume = "2011",
journal = "Electronic Journal of Differential Equations",
issn = "1072-6691",
publisher = "Texas State University - San Marcos",

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Resolvent estimates for elliptic systems in function spaces of higher regularity. / Denk, Robert; Dreher, Michael.

In: Electronic Journal of Differential Equations, Vol. 2011, 109, 2011.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Resolvent estimates for elliptic systems in function spaces of higher regularity

AU - Denk, Robert

AU - Dreher, Michael

PY - 2011

Y1 - 2011

N2 - We consider parameter-elliptic boundary value problems and uniform a priori estimates in L-p-Sobolev spaces of Bessel potential and Besov type. The problems considered are systems of uniform order and mixed-order systems (Douglis-Nirenberg systems). It is shown that compatibility conditions on the data are necessary for such estimates to hold. In particular, we consider the realization of the boundary value problem as an unbounded operator with the ground space being a closed subspace of a Sobolev space and give necessary and sufficient conditions for the realization to generate an analytic semigroup.

AB - We consider parameter-elliptic boundary value problems and uniform a priori estimates in L-p-Sobolev spaces of Bessel potential and Besov type. The problems considered are systems of uniform order and mixed-order systems (Douglis-Nirenberg systems). It is shown that compatibility conditions on the data are necessary for such estimates to hold. In particular, we consider the realization of the boundary value problem as an unbounded operator with the ground space being a closed subspace of a Sobolev space and give necessary and sufficient conditions for the realization to generate an analytic semigroup.

KW - Parameter-ellipticity

KW - Douglis-Nirenberg systems

KW - analytic semigroups

KW - BOUNDARY-VALUE-PROBLEMS

KW - EIGENVALUE ASYMPTOTICS

KW - EQUATIONS

M3 - Article

VL - 2011

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

SN - 1072-6691

M1 - 109

ER -