On the Cauchy problem for a singular parabolic equation (Q2365021)

The author proves the existence of a renormalized solution for the Cauchy problem for the singular parabolic p-Laplacian \(\partial u/\partial t- \text{div} (|\nabla u|^{p-2} \nabla u)=0\) in \(\mathbb{R} ^n \times (0,T),\) where \(T>0,\) \(1<p<2,\) and the initial datum \(u_0 \in L^1 _{\text{loc}}(\mathbb{R}^n)\). No sign restrictions are imposed on \(u_0.\) The proof is based on a priori estimates.