Regularity for degenerate elliptic and parabolic systems

Schwarzacher, Sebastian (2013): Regularity for degenerate elliptic and parabolic systems. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik

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.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: elliptic systems, parabolic systems, power law fluids, BMO estimates, Campanato estimates, non-linear Calderon-Zygmund theory
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Fakultäten: Fakultät für Mathematik, Informatik und Statistik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 14. Oktober 2013
• 1. Bericht­erstatter:in: Diening, Lars