Hölder regularity for porous medium systems

Abstract We establish Hölder continuity for locally bounded weak solutions to certain parabolic systems of porous medium type, i.e. $$\begin{aligned} \partial _t \mathbf{u}-\mathrm{div}(m|\mathbf{u}|^{m-1}D\mathbf{u})=0,\quad m>0. \end{aligned}$$ ∂ t u - div ( m | 1 D ) = 0 , > . As a consequence our local estimates, Liouville type result global is also established. In addition, sufficient conditions are given ensure boundedness solutions.