| Abstract: |
| The infinity Laplacian equation is given by
\[
\Delta_{\infty} u := u_{x_i}u_{x_j}u_{x_ix_j} = 0 \qquad \text{ in } \quad \Omega
\]
where $\Omega$ is an open bounded subset of $\mathbb R^n.$ This equation is a kind of an Euler-Lagrange equation of the variational problem of minimizing the functional
\[
I[v] := \textrm{ess sup} \, |Dv|,
\]
among all Lipschitz continuous functions $v,$ satisfying a prescribed boundary value on $\partial \Omega.$ The infinity obstacle problem is the minimization problem
\[
\min \{ I[v]: v \in W^{1, \infty} , \quad \, v\geq \psi \}
\]
for a given function $\psi \in W^{1, \infty}$ which we refer to as the \emph{obstacle}. In this talk we will discuss an optimal control problem related to the infinity obstacle problem. |
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