An Introduction to Maximal Regularity for Parabolic Evolution Equations
| dc.contributor.author | Denk, Robert | |
| dc.date.accessioned | 2021-11-24T10:11:56Z | |
| dc.date.available | 2021-11-24T10:11:56Z | |
| dc.date.issued | 2021 | eng |
| dc.description.abstract | In this note, we give an introduction to the concept of maximal Lp-regularity as a method to solve nonlinear partial differential equations. We first define maximal regularity for autonomous and non-autonomous problems and describe the connection to Fourier multipliers and R-boundedness. The abstract results are applied to a large class of parabolic systems in the whole space and to general parabolic boundary value problems. For this, both the construction of solution operators for boundary value problems and a characterization of trace spaces of Sobolev spaces are discussed. For the nonlinear equation, we obtain local in time well-posedness in appropriately chosen Sobolev spaces. This manuscript is based on known results and consists of an extended version of lecture notes on this topic. | eng |
| dc.description.version | published | eng |
| dc.identifier.doi | 10.1007/978-981-33-4822-6_1 | eng |
| dc.identifier.uri | https://kops.uni-konstanz.de/handle/123456789/55632 | |
| dc.language.iso | eng | eng |
| dc.rights | terms-of-use | |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | |
| dc.subject | Maximal regularity, Fourier multipliers, Parabolic boundary value problems, Quasilinear evolution equations | eng |
| dc.subject.ddc | 510 | eng |
| dc.title | An Introduction to Maximal Regularity for Parabolic Evolution Equations | eng |
| dc.type | INPROCEEDINGS | eng |
| dspace.entity.type | Publication | |
| kops.citation.bibtex | @inproceedings{Denk2021Intro-55632,
title={An Introduction to Maximal Regularity for Parabolic Evolution Equations},
year={2021},
doi={10.1007/978-981-33-4822-6_1},
isbn={978-981-3348-21-9},
issn={2194-1009},
address={Singapore},
publisher={Springer},
booktitle={Nonlinear Partial Differential Equations for Future Applications},
pages={1--70},
editor={Koike, Shigeaki and Kozono, Hideo and Ogawa, Takayoshi},
author={Denk, Robert}
} | |
| kops.citation.iso690 | DENK, Robert, 2021. An Introduction to Maximal Regularity for Parabolic Evolution Equations. International workshop on Nonlinear Partial Differential Equations for Future Applications, PDEFA 2017. Sendai, Japan, 2. Okt. 2017 - 6. Okt. 2017. In: KOIKE, Shigeaki, Hrsg., Hideo KOZONO, Hrsg., Takayoshi OGAWA, Hrsg. und andere. Nonlinear Partial Differential Equations for Future Applications. Singapore: Springer, 2021, S. 1-70. ISSN 2194-1009. eISSN 2194-1017. ISBN 978-981-3348-21-9. Verfügbar unter: doi: 10.1007/978-981-33-4822-6_1 | deu |
| kops.citation.iso690 | DENK, Robert, 2021. An Introduction to Maximal Regularity for Parabolic Evolution Equations. International workshop on Nonlinear Partial Differential Equations for Future Applications, PDEFA 2017. Sendai, Japan, Oct 2, 2017 - Oct 6, 2017. In: KOIKE, Shigeaki, ed., Hideo KOZONO, ed., Takayoshi OGAWA, ed. and others. Nonlinear Partial Differential Equations for Future Applications. Singapore: Springer, 2021, pp. 1-70. ISSN 2194-1009. eISSN 2194-1017. ISBN 978-981-3348-21-9. Available under: doi: 10.1007/978-981-33-4822-6_1 | eng |
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| kops.conferencefield | International workshop on Nonlinear Partial Differential Equations for Future Applications, PDEFA 2017, 2. Okt. 2017 - 6. Okt. 2017, Sendai, Japan | deu |
| kops.date.conferenceEnd | 2017-10-06 | eng |
| kops.date.conferenceStart | 2017-10-02 | eng |
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| kops.location.conference | Sendai, Japan | eng |
| kops.sourcefield | KOIKE, Shigeaki, Hrsg., Hideo KOZONO, Hrsg., Takayoshi OGAWA, Hrsg. und andere. <i>Nonlinear Partial Differential Equations for Future Applications</i>. Singapore: Springer, 2021, S. 1-70. ISSN 2194-1009. eISSN 2194-1017. ISBN 978-981-3348-21-9. Verfügbar unter: doi: 10.1007/978-981-33-4822-6_1 | deu |
| kops.sourcefield.plain | KOIKE, Shigeaki, Hrsg., Hideo KOZONO, Hrsg., Takayoshi OGAWA, Hrsg. und andere. Nonlinear Partial Differential Equations for Future Applications. Singapore: Springer, 2021, S. 1-70. ISSN 2194-1009. eISSN 2194-1017. ISBN 978-981-3348-21-9. Verfügbar unter: doi: 10.1007/978-981-33-4822-6_1 | deu |
| kops.sourcefield.plain | KOIKE, Shigeaki, ed., Hideo KOZONO, ed., Takayoshi OGAWA, ed. and others. Nonlinear Partial Differential Equations for Future Applications. Singapore: Springer, 2021, pp. 1-70. ISSN 2194-1009. eISSN 2194-1017. ISBN 978-981-3348-21-9. Available under: doi: 10.1007/978-981-33-4822-6_1 | eng |
| kops.title.conference | International workshop on Nonlinear Partial Differential Equations for Future Applications, PDEFA 2017 | eng |
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| source.bibliographicInfo.toPage | 70 | eng |
| source.contributor.editor | Koike, Shigeaki | |
| source.contributor.editor | Kozono, Hideo | |
| source.contributor.editor | Ogawa, Takayoshi | |
| source.flag.etalEditor | true | eng |
| source.identifier.eissn | 2194-1017 | eng |
| source.identifier.isbn | 978-981-3348-21-9 | eng |
| source.identifier.issn | 2194-1009 | eng |
| source.publisher | Springer | eng |
| source.publisher.location | Singapore | eng |
| source.title | Nonlinear Partial Differential Equations for Future Applications | eng |