We show that if u ≥ 0 u \geq 0 , u ∈ L loc m ( Ω ) u \in L_{{\text {loc}}}^m(\Omega ) , Ω ⊂ R n + 1 \Omega \subset {{\mathbf {R}}^{n + 1}} solves ∂ u / ∂ t = Δ u m \partial u/\partial t = \Delta {u^m} , m > 1 m > 1 , in the sense of distributions, then u u is locally Hölder continuous in Ω \Omega .