Holder continuity for degenerate parabolic equations

In this thesis, we will prove the Holder continuity for bounded weak solutions of a large class of degenerate parabolic equations, which are called the porous medium equations. By using auxiliary logarithmic functions, we introduce a new approach that combines both De Giorgi and Moser iteration methods. We consider both the interior and Neumann boundary cases. Then at the end of this thesis, we present some applications to some particular degenerate triangular systems.