Hölder regularity for porous medium systems (Q2048871)

In this paper, the author considers locally bounded weak solutions to certain parabolic systems of porous medium type, i.e. \[ \partial_t u-\mathrm{div}(m|u|^{m-1}Du) = 0, \] with \( m > 0\). As it is well known, everywhere regularity is in general not expected from systems of elliptic or parabolic type, nevertheless, the special quasi-diagonal structure of thus system, enables the author to achieve the Hölder regularity of locally bounded solutions. As a consequence of the local Hölder estimates, a Liouville type result for bounded global solutions is also established. In addition, sufficient conditions are given to ensure local boundedness of local weak solutions.