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- W2949203736 abstract "The Dirichlet problem $$ begin{cases} Delta_{infty}u-|Du|^2=0 quad text{on $Omegasubset Rset ^n$} u|_{partial Omega}=g end{cases} $$ might have many solutions, where $Delta_{infty}u=sum_{1leq i,jleq n}u_{x_i}u_{x_j}u_{x_ix_j}$. In this paper, we prove that the maximal solution is the unique absolute minimizer for $H(p,z)={1over 2}|p|^2-z$ from calculus of variations in $L^{infty}$ and the minimal solution is the continuum value function from the tug-of-war game. We will also characterize graphes of solutions which are neither an absolute minimizer nor a value function. A remaining interesting question is how to interpret those intermediate solutions. Most of our approaches are based on an idea of Barles-Busca [BB]." @default.
- W2949203736 created "2019-06-27" @default.
- W2949203736 creator A5060637951 @default.
- W2949203736 date "2009-06-03" @default.
- W2949203736 modified "2023-09-27" @default.
- W2949203736 title "Maximal and minimal solutions of an Aronsson equation: $L^{infty}$ variational problems versus the game theory" @default.
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