Variational Estimates for Nonnegative Harmonic Functions

2026/07/29 by Jakob Fromherz
Mathematics · #math.AP #msc:31B05 #msc:31B10 #msc:31B25 #msc:31B35

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arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

Consider a nonnegative harmonic function u on a domain D⊂ℝ^d-1. We establish boundedness of Jones' variational integral on an ultradense, d-1 dimensional subset of the boundary of C^1,Dini domains. This result was previously only known for the unit ball.

Citations

• Bounding Radial Variation of positive harmonic Functions on Lipschitz Domains
• Radial Variation of Positive Harmonic Functions on Lipschitz Domains

Related

• Expansion of harmonic functions near the boundary of Dini domains
• Bounding Radial Variation of positive harmonic Functions on Lipschitz Domains
• A note on the critical set of harmonic functions near the boundary
• Fatou's theorem for subordinate Brownian motions with Gaussian\n components on C^1,1 open sets
• Radial Variation of Positive Harmonic Functions on Lipschitz Domains