Overdetermined problems for the normalized p-Laplacian

2017/11/23 by Agnid Banerjee, Banerjee, Agnid, Bernd Kawohl +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1711.08696

revised version ( a few typos corrected)

openalex publication_date 2017/11/23 · arxiv created 2018/01/05 · arxiv updated 2018/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the symmetry result of Serrin and Weinberger from the Laplacian operator to the highly degenerate game-theoretic p-Laplacian operator and show that viscosity solutions of -Δ_p^Nu=1 in Ω, u=0 and \tfrac∂ u∂ν=-c≠ 0 on ∂Ω can only exist on a bounded domain Ω if Ω is a ball.

Citations

• A symmetry problem in potential theory
• A Symmetry Result Related to Some Overdetermined Boundary Value Problems

Related

• Asymptotics for the resolvent equation associated to the game-theoretic p-laplacian
• Asymptotic analysis of solutions related to the game-theoretic p-laplacian
• Game theoretical asymptotic mean value properties for non-homogeneous p-Laplace problems
• C^1,α regularity for the normalized p-Poisson problem
• Overdetermined boundary value problems for the ∞-Laplacian