The time derivative in a singular parabolic equation. (Q2402131)

In this paper, the author considers the \(p\)-Laplacean evolution equation \[u_t=\Delta_pu\] with \(1<p<2\) and he is able to prove that the solutions have a first order time derivative \(u_t\) in Sobolev's sense. This is very interesting because, by using the celebrated methods by DeGiorgi, Nash, and Moser, it is possible to prove the regularity of the space derivatives but it is impossible to treat directly the time derivative which is regarded as merely a distribution.