Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries

DOI10.1090/tran/6927zbMath1373.31003arXiv1507.02039OpenAlexW1488909951MaRDI QIDQ5347277

Murat Akman, Matthew Badger, José Maria Martell, Steven Hofmann

Publication date: 23 May 2017

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.02039

zbMATH Keywords

harmonic measurerectifiability1-sided non-tangentially accessible domainsAhlfors-David regular boundaries

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Length, area, volume, other geometric measure theory (28A75) Boundary behavior of harmonic functions in higher dimensions (31B25)

Related Items (13)

Rectifiability of harmonic measure ⋮ Sets of absolute continuity for harmonic measure in NTA domains ⋮ \(A_\infty\) implies NTA for a class of variable coefficient elliptic operators ⋮ On harmonic measure and rectifiability in uniform domains ⋮ Absolute continuity of harmonic measure for domains with lower regular boundaries ⋮ Boundary rectifiability and elliptic operators with \(W^{1, 1}\) coefficients ⋮ Tangent measures of elliptic measure and applications ⋮ \(L^2\)-boundedness of gradients of single-layer potentials and uniform rectifiability ⋮ Uniform rectifiability and elliptic operators satisfying a Carleson measure condition ⋮ Gradient of the single layer potential and quantitative rectifiability for general Radon measures ⋮ Elliptic measures and square function estimates on 1-sided chord-arc domains ⋮ Square function estimates, the BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets ⋮ Approximate tangents, harmonic measure, and domains with rectifiable boundaries

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