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

Abstract

We show that if ⊂ ‫ޒ‬ 3 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 , then the outer unit normal to ∂ 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.

Locations

• Analysis & PDE - View
• arXiv (Cornell University) - View - PDF
• Project Euclid (Cornell University) - View - PDF
• DataCite API - View