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# An Introduction to Maximal Regularity for Parabolic Evolution Equations

Type of Publication: | Contribution to a conference collection |

Publication status: | Published |

Author: | Denk, Robert |

Year of publication: | 2021 |

Conference: | International workshop on Nonlinear Partial Differential Equations for Future Applications, PDEFA 2017, Oct 2, 2017 - Oct 6, 2017, Sendai, Japan |

Published in: | Nonlinear Partial Differential Equations for Future Applications / Koike, Shigeaki; Kozono, Hideo; Ogawa, Takayoshi et al. (ed.). - Singapore : Springer, 2021. - pp. 1-70. - ISSN 2194-1009. - eISSN 2194-1017. - ISBN 978-981-3348-21-9 |

DOI (citable link): | https://dx.doi.org/10.1007/978-981-33-4822-6_1 |

Summary: |
In this note, we give an introduction to the concept of maximal L
^{p}-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. |

Subject (DDC): | 510 Mathematics |

Keywords: | Maximal regularity, Fourier multipliers, Parabolic boundary value problems, Quasilinear evolution equations |

Bibliography of Konstanz: | Yes |

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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, 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

@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} }