Resolvent estimates for elliptic systems in function spaces of higher regularity

Resolvent estimates for elliptic systems in function spaces of higher regularity

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 o...

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Main Authors: Robert Denk, Michael Dreher
Format: Article
Language:English
Published: Texas State University 2011-08-01
Series:Electronic Journal of Differential Equations
Subjects:
Parameter-ellipticity
Douglis-Nirenberg systems
analytic semigroups
Online Access:http://ejde.math.txstate.edu/Volumes/2011/109/abstr.html
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spelling doaj-a2639b40abad4c8ba3bd853c21bdd94a2020-11-24T21:06:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-08-012011109,112Resolvent estimates for elliptic systems in function spaces of higher regularityRobert DenkMichael DreherWe 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. http://ejde.math.txstate.edu/Volumes/2011/109/abstr.htmlParameter-ellipticityDouglis-Nirenberg systemsanalytic semigroups
collection DOAJ
language English
format Article
sources DOAJ
author Robert Denk
Michael Dreher
spellingShingle Robert Denk
Michael Dreher
Resolvent estimates for elliptic systems in function spaces of higher regularity
Electronic Journal of Differential Equations
Parameter-ellipticity
Douglis-Nirenberg systems
analytic semigroups
author_facet Robert Denk
Michael Dreher
author_sort Robert Denk
title Resolvent estimates for elliptic systems in function spaces of higher regularity
title_short Resolvent estimates for elliptic systems in function spaces of higher regularity
title_full Resolvent estimates for elliptic systems in function spaces of higher regularity
title_fullStr Resolvent estimates for elliptic systems in function spaces of higher regularity
title_full_unstemmed Resolvent estimates for elliptic systems in function spaces of higher regularity
title_sort resolvent estimates for elliptic systems in function spaces of higher regularity
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2011-08-01
description 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.
topic Parameter-ellipticity
Douglis-Nirenberg systems
analytic semigroups
url http://ejde.math.txstate.edu/Volumes/2011/109/abstr.html
work_keys_str_mv AT robertdenk resolventestimatesforellipticsystemsinfunctionspacesofhigherregularity
AT michaeldreher resolventestimatesforellipticsystemsinfunctionspacesofhigherregularity
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