Pingen, Michael:
Zur Regulierungstheorie elliptischer Systeme und harmonischer Abbildungen
Duisburg, 2006
Dissertation2006Mathematik
Fakultät für Mathematik
Titel:
Zur Regulierungstheorie elliptischer Systeme und harmonischer Abbildungen
Autor(in):
Pingen, Michael
Erscheinungsort
Duisburg
Erscheinungsjahr
2006
Umfang
110 Bl.
DuEPublico ID:
URN:
Signatur der UB
Notiz:
Duisburg, Essen, Univ., Diss., 2006

Abstract:

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.