Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions

By Carlos E.Kenig, David Preiss, T. Toro. 2007

64 citations recorded by the source corpus.

In this work we introduce the use of powerful tools from geometric measure theory (GMT) to study problems related to the size and structure of sets of mutual absolute continuity for the harmonic measure $ \omega^+$ of a domain $ \Omega=\Omega^+\subset\mathbb{R}^n$ and the harmonic measure $ \omega^-$ of $ \Omega^-$, $ \Omega^-=$int$ (\Omega^c)$, in dimension $ n\ge 3$.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3bf294e2d3d1a0fe7edf14e53541724483673366

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Kaj Nyström
2. John L. Lewis
3. Verena Bogelein
4. Frank Duzaar
5. Giuseppe Mingione
6. S. Hofmann
7. J. M. Martell
8. Sun-Sig Byun

In Computational Theory and Mathematics

1. Kaj Nyström
2. John L. Lewis
3. Verena Bogelein
4. Frank Duzaar
5. Giuseppe Mingione
6. S. Hofmann
7. Sun-Sig Byun
8. Lihe Wang

In Mathematical Physics

1. Kaj Nyström
2. John L. Lewis
3. Juan Luis V'azquez
4. Xixia Ma

Citations in the corpus

• Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited (2010, unknown): “In [9] Kenig, Preiss and Toro used the tangent measures of harmonic measure to demonstrateH– dimω = H– dimω = n−1 on every 2-sided NTA domain Ω ⊂ R (n ≥ 3) with ω ≪ ω ≪ ω.”
• Regularity and Free Boundary Regularity for the p-Laplace Operator in Reifenberg Flat and Ahlfors Regular Domains (2012, background): “We note that a problem related to Theorem 4 was considered in [21] and [3].”