Phragmén-Lindelöf theorems and p-harmonic measures for sets near low-dimensional hyperplanes

2015/03/18 by Niklas L. P. Lundström, Lundström, Niklas L. P. · 2 citations
Computer Science · Mathematics · #35J25 #35J60 #35J70 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #math.AP #msc:35J25 #msc:35J60 #msc:35J70

paper · pdf · doi:10.48550/arxiv.1503.05382

openalex publication_date 2015/03/18 · arxiv created 2015/12/03 · arxiv updated 2015/12/04 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We prove estimates of a p-harmonic measure, p ∈ (n-m, ∞], for sets in Rⁿ which are close to an m-dimensional hyperplane Λ⊂ Rⁿ, m ∈ [0,n-1]. Using these estimates, we derive results of Phragmén-Lindelöf type in unbounded domains Ω⊂ Rⁿ∖ Λ for p-subharmonic functions. Moreover, we give local and global growth estimates for p-harmonic functions, vanishing on sets in Rⁿ, which are close to an m-dimensional hyperplane.

Cited by

• Estimates for viscosity solutions of fully nonlinear equations near smooth boundaries
• Phragmén-Lindelöf-type theorems for functions in Homogeneous De Giorgi Classes

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