Sets of absolute continuity for harmonic measure in NTA domains

DOI10.1007/s11118-016-9550-5zbMath1361.31006arXiv1410.2782OpenAlexW2963990552MaRDI QIDQ334897

Jonas Azzam

Publication date: 1 November 2016

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.2782

zbMATH Keywords

harmonic measureHausdorff measurecorkscrew condition

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Hausdorff and packing measures (28A78) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items

Rectifiability of harmonic measure, On harmonic measure and rectifiability in uniform domains, A two-phase free boundary problem for harmonic measure and uniform rectifiability, Absolute continuity of harmonic measure for domains with lower regular boundaries, Tangent measures of elliptic measure and applications, Conformal transformation of uniform domains under weights that depend on distance to the boundary, Approximate tangents, harmonic measure, and domains with rectifiable boundaries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rectifiability of harmonic measure
• A new characterization of chord-arc domains
• The weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability
• The one-phase problem for harmonic measure in two-sided NTA domains
• Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited
• Distortion of the boundary under conformal mapping
• Harmonic measure and arclength
• Wolff snowflakes
• Morceaux de graphes lipschitziens et intégrales singulières sur une surface
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• On singularity of harmonic measure in space
• Estimates of harmonic measure
• Elliptic partial differential equations of second order
• Non-homogeneous \(Tb\) theorem and random dyadic cubes on metric measure spaces
• Hard Sard: quantitative implicit function and extension theorems for Lipschitz maps
• Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$
• On weak reverse hölder inequalities for nondoubling harmonic measures
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• Approximate tangents, harmonic measure, and domains with rectifiable boundaries
• Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries
• Potential theory