Droplet spreading under weak slippage: A basic result on finite speed of propagation

We prove a new qualitative result on finite speed of propagation for the thin film equation subjected to Navier slippage or even weaker slip conditions. Our approach works in multiple space dimensions and is based on a novel technique which combines recently established weighted energy estimates with a Hardy-type inequality and with Stampacchia's iteration lemma. It can be adapted to degenerate parabolic equations of order different from four as well.