On Regularity of the Time Derivative for Degenerate Parabolic Systems
Jens Frehse, Sebastian Schwarzacher · SIAM Journal on Mathematical Analysis · 2015
We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) $p$-Laplace system and models for non-Newtonian fluids of powerlaw or Carreau type. By the use of special weak different quotients adapted to the variational structure we bound fractional derivatives of $u_t$ in time and space directions. Although the estimates presented here are valid under very general assumptions they are a novelty even for the parabolic $p$-Laplace equation.