Abstract / Description of output
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 language | English |
|---|---|
| Pages (from-to) | 559–588 |
| Number of pages | 31 |
| Journal | Analysis & PDE |
| Volume | 10 |
| Issue number | 3 |
| Publication status | Published - 17 Apr 2017 |
| Externally published | Yes |