Weak Solutions of the Porous Medium Equation
Björn E. J. Dahlberg, Carlos E. Kenig · Transactions of the American Mathematical Society · 1993
We show that if $u \geq 0$, $u \in L_{{\text {loc}}}^m(\Omega )$, $\Omega \subset {{\mathbf {R}}^{n + 1}}$ solves $\partial u/\partial t = \Delta {u^m}$, $m > 1$ , in the sense of distributions, then $u$ is locally Hölder continuous in $\Omega$.