Gradient estimates for doubly nonlinear parabolic equations

The local gradient estimates for weak solutions of equation
$$ u_t-\operatorname{div}\{|u|^l|Du|^{m-2}Du\}=0 $$
are established in the case $m>1$, $0\le l<1$. In the case $m>1$, $l\ge1$ some weight gradient estimates are obtained. Bibl. 19 titles.