Abstract:In this note, we show that a natural optimal control problem for the
∞
\infty
-obstacle problem admits an optimal control which is also an optimal state. Moreover, we show the convergence of the minimal value of an optimal control problem for the
p
p
-obstacle problem to the minimal value of our optimal control problem for the
∞
\infty
-obstacle problem, as
p
→
∞
p\to \infty
.
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