An exterior overdetermined problem for Finsler $N$-laplacian in convex cones

Giulio Ciraolo; Xiaoliang Li

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arXiv · 2111.09796

An exterior overdetermined problem for Finsler $N$-laplacian in convex cones

Giulio Ciraolo·Xiaoliang Li

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Abstract

We consider a partially overdetermined problem for anisotropic $N$-Laplace equations in a convex cone $Σ$ intersected with the exterior of a bounded domain $Ω$ in $\mathbb{R}^N$, $N\geq 2$. Under a prescribed logarithmic condition at infinity, we prove a rigidity result by showing that the existence of a solution implies that $Σ\capΩ$ must be the intersection of the Wulff shape and $Σ$. Our approach is based on a Pohozaev-type identity and the characterization of minimizers of the anisotropic isoperimetric inequality inside convex cones.

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Giulio Ciraolo, Xiaoliang Li. 2021-11-18. An exterior overdetermined problem for Finsler $N$-laplacian in convex cones. https://arxiv.org/abs/2111.09796

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