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arXiv · 1903.08520

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

Fredrik Arbo Høeg·Eero Ruosteenoja
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Abstract

We show that value functions of a certain time-dependent control problem in $Ω\times (0,T)$, with a continuous payoff $F$ on the parabolic boundary, converge uniformly to the viscosity solution of the parabolic dominative $p$-Laplace equation $$2(n+p)u_t=Δu+(p-2)λ_n(D^2 u),$$ with the boundary data $F$. Here $2\leq p< \infty$, and $λ_n(D^2 u)$ is the largest eigenvalue of the Hessian $D^2 u$.

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Fredrik Arbo Høeg, Eero Ruosteenoja. 2020-01-09. A control problem related to the parabolic dominative $p$-Laplace equation. https://arxiv.org/abs/1903.08520

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