On maximal regularity for a class of evolutionary equations

Rainer Picard, Sascha Trostorff, Marcus Waurick

Research output: Contribution to journal › Article

Abstract

The issue of so-called maximal regularity is discussed within a Hilbert space framework for a class of evolutionary equations. Viewing evolutionary equations as a sum of two unbounded operators, showing maximal regularity amounts to establishing that the operator sum considered with its natural domain is already closed. For this we use structural constraints of the coefficients rather than semi-group strategies or sesqui-linear form methods, which would be difficult to come by for our general problem class. Our approach, although limited to the Hilbert space case, complements known strategies for approaching maximal regularity and extends them in a different direction. The abstract findings are illustrated by re-considering some known maximal regularity results within the framework presented.
LanguageEnglish
Pages1368-1381
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume449
Issue number2
Early online date28 Dec 2016
DOIs
Publication statusPublished - 15 May 2017

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Maximal Regularity
Hilbert spaces
Hilbert space
Unbounded Operators
Linear Forms
Semigroup
Complement
Closed
Class
Coefficient
Operator
Framework
Strategy

Keywords

  • maximal regularity
  • evolutionary equations
  • material laws
  • coupled systems

Cite this

Picard, Rainer ; Trostorff, Sascha ; Waurick, Marcus. / On maximal regularity for a class of evolutionary equations. In: Journal of Mathematical Analysis and Applications. 2017 ; Vol. 449, No. 2. pp. 1368-1381.
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Picard, R, Trostorff, S & Waurick, M 2017, 'On maximal regularity for a class of evolutionary equations' Journal of Mathematical Analysis and Applications, vol. 449, no. 2, pp. 1368-1381. https://doi.org/10.1016/j.jmaa.2016.12.057

On maximal regularity for a class of evolutionary equations. / Picard, Rainer; Trostorff, Sascha; Waurick, Marcus.

In: Journal of Mathematical Analysis and Applications, Vol. 449, No. 2, 15.05.2017, p. 1368-1381.

Research output: Contribution to journal › Article

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Picard R, Trostorff S, Waurick M. On maximal regularity for a class of evolutionary equations. Journal of Mathematical Analysis and Applications. 2017 May 15;449(2):1368-1381. https://doi.org/10.1016/j.jmaa.2016.12.057

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