On a time-depending Monge-Ampère type equation

In this paper, we prove a comparison result between a solution u(x, t), x is an element of Omega subset of R-2, t is an element of (0, T), of a time depending equation involving the Monge-Ampere operator in the plane and the solution of a conveniently symmetrized parabolic equation. To this aim, we prove a derivation formula for the integral of a smooth function g(x, t) over sublevel sets of u, {x is an element of Omega : u(x, t) < nu}, nu is an element of R, having the same perimeter in R-2. (C) 2012 Elsevier Ltd. All rights reserved.