We study the Evolutionary $p$-Laplace Equation in the singular case $1 < p < 2$. We prove that a weak solution has a time derivative (in Sobolev's sense) which is a function belonging (locally) to a $L^q$-space.
Peter Lindqvist. "The time derivative in a singular parabolic equation." Differential Integral Equations 30 (9/10) 795 - 808, September/October 2017. https://doi.org/10.57262/die/1495850427