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-Ampre 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)
Brandolini B. (2012). On a time-depending Monge-Ampère type equation. NONLINEAR ANALYSIS, 75(10), 4006-4013 [10.1016/j.na.2012.02.016].
On a time-depending Monge-Ampère type equation
Brandolini B.
2012-01-01
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-Ampre 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)
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