Regularity for degenerate elliptic and parabolic systems

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

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)
• 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
• Signature of the printed copy: 0001/UMC 21605