Inserted: 13 nov 2009
Last Updated: 4 mar 2010
We consider overdetermined boundary value problems for the $\infty$-Laplacian in a domain $\Omega$ of $*R*^n$ and discuss what kind of implications on the geometry of $\Omega$ the existence of a solution may have. The classical $\infty$-Laplacian, the normalized or game-theoretic $\infty$-Laplacian and the limit of the $p$-Laplacian as $p\to\infty$ are considered and provide different answers.
Keywords: viscosity solution, overdetermined bvp, degenerate elliptic equation, web-function, cut locus, ridge set