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Regularity for degenerate elliptic and parabolic systems
Regularity for degenerate elliptic and parabolic systems
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.
elliptic systems, parabolic systems, power law fluids, BMO estimates, Campanato estimates, non-linear Calderon-Zygmund theory
Schwarzacher, Sebastian
2013
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Schwarzacher, Sebastian (2013): Regularity for degenerate elliptic and parabolic systems. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics
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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.