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

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Schwarzacher_Sebastian.pdf 813kB 
Abstract
In this work local behavior for solutions to the inhomogeneous pLaplace in divergence form and its parabolic version are studied. It is parabolic and nonlinear generalization of the CalderonZygmund 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 pLaplace and the parabolic pLaplace system. An adaption of some estimates to fluid mechanics, namely on the pStokes equation are also proven. The pStokes system is a very important physical model for socalled non Newtonian fluids (e.g. blood). For this system BMO and Hoelder estimates are proven in the stationary 2dimensional case.
Item Type:  Theses (Dissertation, LMU Munich) 

Keywords:  elliptic systems, parabolic systems, power law fluids, BMO estimates, Campanato estimates, nonlinear CalderonZygmund 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 PDFfile:  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 