The one-phase problem for harmonic measure in two-sided NTA domains

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


We show that if ω ⊂ R3 is a two-sided NTA domain with AD-regular boundary such that the logarithm of the Poisson kernel belongs to VMO(σ), where σ is the surface measure of ω, then the outer unit normal to ∂ω belongs to VMO(σ) too. The analogous result fails for dimensions larger than 3. This answers a question posed by Kenig and Toro and also by Bortz and Hofmann.
Original languageEnglish
Pages (from-to)559-588
JournalAnalysis and PDE
Issue number3
Publication statusPublished - 1 Jan 2017


  • Free boundary problem
  • Harmonic measure
  • Nontangentially accessible (NTA) domains
  • Poisson kernel
  • VMO


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