A control problem related to the parabolic dominative p-Laplace equation

Abstract

We show that value functions of a certain time-dependent control problem in Ω × (0, T), with a continuous payoff F on the parabolic boundary, converge uniformly to the viscosity solution of the parabolic dominative p-Laplace equation 2(n + p)ut = ∆u + (p − 2)λn(D2u), with the boundary data F. Here 2 < p < ∞, and λn(D2u) is the largest eigenvalue of the Hessian D2u.