A partially overdetermined problem for p-Laplace equation in convex cones

2023/10/09 by Ma, Hui, Yang, Mingxuan, Yin, Jiabin
#31B15 #35A23 #35N25 #53C24 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.05739

Abstract

We consider a partially overdetermined problem for the p-Laplace equation in a convex cone C intersected with the exterior of a smooth bounded domain Ω in ℝⁿ(n≥2). First, we establish the existence, regularity, and asymptotic behavior of a capacitary potential. Then, based on these properties of the potential, we use a P-function, the isoperimetric inequality, and the Heintze-Karcher type inequality in a convex cone to obtain a rigidity result under the assumption of orthogonal intersection.

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