Analysis of the free boundary for the $p$-parabolic variational problem $(p\ge 2)$

Variational inequalities (free boundaries), governed by the p -parabolic equation ( p\geq 2 ), are the objects of investigation in this paper. Using intrinsic scaling we establish the behavior of solutions near the free boundary. A consequence of this is that the time levels of the free boundary are porous (in N -dimension) and therefore its Hausdorff dimension is less than N . In particular the N -Lebesgue measure of the free boundary is zero for each t -level.