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  Regularity for evolution equations with non-autonomous perturbations in Banach spaces

Penz, M. (2018). Regularity for evolution equations with non-autonomous perturbations in Banach spaces. Journal of Mathematical Physics, 59(10): 103512. doi:10.1063/1.5011306.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0002-7FF2-F Version Permalink: http://hdl.handle.net/21.11116/0000-0004-93D2-8
Genre: Journal Article

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 Creators:
Penz, M.1, Author              
Affiliations:
1Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              

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 Abstract: We provide regularity of solutions to a large class of evolution equations on Banach spaces where the generator is composed of a static principal part plus a non-autonomous perturbation. Regularity is examined with respect to the graph norm of the iterations of the principal part. The results are applied to the Schrödinger equation and conditions on a time-dependent scalar potential for the regularity of the solution in higher Sobolev spaces are derived.

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Language(s): eng - English
 Dates: 2017-10-312018-10-122018-10-312018-10
 Publication Status: Published in print
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 Rev. Method: Peer
 Identifiers: DOI: 10.1063/1.5011306
arXiv: 1801.03361
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Project name : With special thanks to Jonas Lampart for pointing out the studies of Schmid–Griesemer, as well as to Michael Ruggenthaler and Eric Stachura for helpful discussions. An anonymous referee spotted a critical flaw in the Proof of Lemma III.4, that in the course led to the new Defini- tion III.1 and Lemma III.3, and helped to improve the manuscript substantially. This work was supported by the Erwin Schr ̈ odinger Fellowship No. J 4107-N27 of the FWF (Austrian Science Fund).
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Title: Journal of Mathematical Physics
Source Genre: Journal
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Publ. Info: Woodbury, N.Y. [etc.] : American Institute of Physics
Pages: - Volume / Issue: 59 (10) Sequence Number: 103512 Start / End Page: - Identifier: ISSN: 0022-2488
CoNE: https://pure.mpg.de/cone/journals/resource/954922836227