Uniqueness and nonuniqueness of p-harmonic Green functions on weighted Rⁿ and metric spaces

2025/05/25 by Anders Björn, Björn, Anders, Jana Björn +5
Computer Science · Mathematics · #31C45 #31E05 #35J92 #49Q20 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary: 35J08 #Secondary: 30L99

paper · pdf · doi:10.48550/arxiv.2505.19074

openalex publication_date 2025/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We study uniqueness of p-harmonic Green functions in domains Ω in a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality, with 1

Citations

• Inverse limit spaces satisfying a Poincare inequality
• Modulus and the Poincar� inequality on metric measure spaces
• Quasiconformal maps in metric spaces with controlled geometry

Related

• Green function in metric measure spaces
• Doubling measures and Poincaré inequalities for sphericalizations of metric spaces
• L_f^p harmonic 1-forms on complete non-compact smooth metric measure spaces
• Harmonic functions on metric measure spaces
• Characterization of mean value harmonic functions on norm induced metric measure spaces with weighted Lebesgue measure