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arXiv · 0911.2576

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

G. Buttazzo·B. Kawohl
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Abstract

We consider overdetermined boundary value problems for the $\infty$-Laplacian in a domain $Ω$ of $\R^n$ and discuss what kind of implications on the geometry of $Ω$ 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.

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G. Buttazzo, B. Kawohl. 2010-03-04. Overdetermined boundary value problems for the $\infty$-Laplacian. https://arxiv.org/abs/0911.2576

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