Search results for "Derivation formula"

On a time-depending Monge-Ampère type equation

2012

Abstract In this paper, we prove a comparison result between a solution u ( x , t ) , x ∈ Ω ⊂ R 2 , t ∈ ( 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 ∈ Ω : u ( x , t ) ϑ } , ϑ ∈ R , having the same perimeter in R 2 .