ε-Approximability of Harmonic Functions in Lᵖ Implies Uniform Rectifiability
Bortz, Simon · Tapiola, Olli
Original · EN
Suppose that Ω⊂ Rⁿ⁺¹, n ≥ 2, is an open set satisfying the corkscrew condition with an n-dimensional ADR boundary, ∂ Ω. In this note, we show that if harmonic functions are ε-approximable in Lᵖ for any p > n/(n-1), then ∂ Ω is uniformly rectifiable. Combining our results with those in [HT] (Hofmann-Tapiola) gives us a new characterization of uniform rectifiability which complements the recent results in [HMM] (Hofmann-Martell-Mayboroda), [GMT] (Garnett-Mourgoglou-Tolsa) and [AGMT] (Azzam-Garnett-Mourgoglou-Tolsa).
English translation
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