An exterior overdetermined problem for Finsler N-Laplacian in convex cones

We consider a partially overdetermined problem for anisotropic N-Laplace equations in a convex cone Sigma intersected with the exterior of a bounded domain Omega in R-N, N >= 2. Under a prescribed logarithmic condition at infinity, we prove a rigidity result by showing that the existence of a solution implies that Sigma boolean AND Omega must be the intersection of the Wulff shape and Sigma. Our approach is based on a Pohozaev-type identity and the characterization of minimizers of the anisotropic isoperimetric inequality inside convex cones.

Automated summary

In this paper, the authors consider a partially overdetermined problem for anisotropic N-Laplace equations in a convex cone. They prove the existence of a solution and a rigidity result using a prescribed logarithmic condition and the characterization of minimizers of anisotropic isoperimetric inequality inside convex cones.