Regularity for degenerate nonlinear parabolic partial differential equations

This dissertation studies regularity and existence questions related to nonlinear parabolic partial differential equations. The thesis consists of an overview and four research papers. The emphasis is on certain doubly nonlinear equations that are important in several applications. We study the Hölder continuity of weak solutions and the local boundedness of their gradients by modifying and extending known arguments for other similar equations. We also consider an existence question for a parabolic obstacle problem. In particular, we show that the obstacle problem with a continuous obstacle admits a unique continuous solution up to the boundary, provided the domain is smooth enough.