This thesis deals with regualrity questions of elliptic and parabolic systems of partial differential equations of second order. With the help of a Harnack inequality it is shown that bounded weak solutions of certain parabolic systems are Hölder continous. In the second chapter we prove regularity theorems for weak harmonic mappings in the interior and at the boundary, an important tool for these theorems are again two Harnack inequalities. The last two chapters deal with degenerate elliptic systems, for certain degenerate elliptic coefficients (e.g. in the Muckenhouptclass A2) we prove two Harnack inequalities and show with these inequalities some regularity theorems for degenerate elliptic systems.
| Identifer | oai:union.ndltd.org:DUETT/oai:DUETT:duett-05102006-125225 |
| Date | 11 May 2006 |
| Creators | Pingen, Michael |
| Contributors | Prof. Dr. Heiko von der Mosel, Prof. Dr. Ulrich Dierkes |
| Publisher | Gerhard-Mercator-Universitaet Duisburg |
| Source Sets | Dissertations and other Documents of the Gerhard-Mercator-University Duisburg |
| Language | German |
| Detected Language | English |
| Type | text |
| Format | application/pdf, text/html |
| Source | http://www.ub.uni-duisburg.de/ETD-db/theses/available/duett-05102006-125225/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. Hiermit erteile ich der Universitaet Duisburg das nicht-ausschliessliche Recht unter den unten angegebenen Bedingungen, meine Dissertation, Staatsexamens- oder Diplomarbeit, meinen Forschungs- oder Projektbericht zu veroeffentlichen und zu archivieren. Ich behalte das Urheberrecht und das Recht das Dokument zu veroeffentlichen und in anderen Arbeiten weiterzuverwenden. |
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