The time derivative in a singular parabolic equation. (English) Zbl 1424.35235

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.


35K67 Singular parabolic equations
35K92 Quasilinear parabolic equations with \(p\)-Laplacian
35B45 A priori estimates in context of PDEs
Full Text: arXiv