Schwarzacher, Sebastian (2013): Regularity for degenerate elliptic and parabolic systems. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics |

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**DOI**: 10.5282/edoc.16209

### Abstract

In this work local behavior for solutions to the inhomogeneous p-Laplace in divergence form and its parabolic version are studied. It is parabolic and non-linear generalization of the Calderon-Zygmund theory for the Laplace operator. I.e. the borderline case BMO is studied. The two main results are local BMO and Hoelder estimates for the inhomogenious p-Laplace and the parabolic p-Laplace system. An adaption of some estimates to fluid mechanics, namely on the p-Stokes equation are also proven. The p-Stokes system is a very important physical model for so-called non Newtonian fluids (e.g. blood). For this system BMO and Hoelder estimates are proven in the stationary 2-dimensional case.

Item Type: | Theses (Dissertation, LMU Munich) |
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Keywords: | elliptic systems, parabolic systems, power law fluids, BMO estimates, Campanato estimates, non-linear Calderon-Zygmund theory |

Subjects: | 500 Natural sciences and mathematics 500 Natural sciences and mathematics > 510 Mathematics |

Faculties: | Faculty of Mathematics, Computer Science and Statistics |

Language: | English |

Date of oral examination: | 14. October 2013 |

1. Referee: | Diening, Lars |

MD5 Checksum of the PDF-file: | d4bae25e781baa5f7395f3969bb71fb4 |

Signature of the printed copy: | 0001/UMC 21605 |

ID Code: | 16209 |

Deposited On: | 07. Nov 2013 14:21 |

Last Modified: | 24. Oct 2020 00:22 |