Overdetermined boundary value problems for the ∞-Laplacian

الأصل · EN

We consider overdetermined boundary value problems for the ∞-Laplacian in a domain Ω of ⁿ and discuss what kind of implications on the geometry of Ω the existence of a solution may have. The classical ∞-Laplacian, the normalized or game-theoretic ∞-Laplacian and the limit of the p-Laplacian as p→ ∞ are considered and provide different answers.