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

Abstract

We consider overdetermined boundary value problems for the $\infty$-Laplacian in a domain $\Omega$ of ${\mathbb{R}}^n$ 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.

9 pages, 1 figure

References in corpus (1)

• Uniqueness of values of Aronsson operators and running costs in "tug-of-war" games

Cited by in corpus (1)

• On the Dirichlet and Serrin problems for the inhomogeneous infinity Laplacian in convex domains: Regularity and geometric results