| We study the existence, uniqueness and the regularity of solutions of the equation ft = Deltapf = div (|Df|p -2Df) under bourdary conditions f = 0 and |Df| = 1. We show that if the function u is concave and of class C1,alpha with bounded support at the initial time, then the problem admits a unique solution which exists until vanishing identically. Furthermore, the boundary of the support of u is smooth for all positive time. |
