Overdetermined boundary value problems for the $\infty$-Laplacian

G. Buttazzo, B. Kawohl

Published 2009-11-13, updated 2010-03-04Version 3

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.