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On spectral theory, control, and higher regularity of infinite-dimensional operator equations
Citation Link: https://doi.org/10.15480/882.5197
Publikationstyp
Doctoral Thesis
Date Issued
2023
Sprache
English
Author(s)
Gabel, Fabian Nuraddin Alexander
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2023-06-09
Institut
TORE-DOI
Citation
Technische Universität Hamburg (2023)
This work studies different physically motivated mathematical models. For discrete periodic Schrödinger operators, we derive sufficient conditions on the applicability of the finite section method. We derive an abstract theorem for non-autonomous Cauchy problems with time-dependent observation families to assure final-state observability. Furthermore, we prove necessary and sufficient geometric conditions on the family of observation sets in the case of non-autonomous diffusion problems. For the Navier-Stokes equations on planar Lipschitz domains, we prove higher regularity of Leray-Hopf solutions in spaces of Lebesgue functions and distributions. To this end, we develop a functional analytic framework for the Stokes operator on Lebesgue spaces, including a proof of maximal regularity and boundedness of the H-infinity-calculus. Furthermore, we characterize the domains of fractional powers of the Stokes operator on Lp-spaces in terms of Bessel-potential spaces.
DDC Class
510: Mathematik
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Gabel_Fabian_On-spectral-theory-control-and-higher-regularity-of-infinite-dimensional-operator-equations.pdf
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