Square functions, nontangential limits, and harmonic measure in codimension larger than 1

DOI10.1215/00127094-2020-0048zbMath1471.31001arXiv1808.08882OpenAlexW3115046559MaRDI QIDQ2037838

Guy David, Max Engelstein, Svitlana Mayboroda

Publication date: 8 July 2021

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.08882

zbMATH Keywords

harmonic measuredegenerate elliptic equationsrectifiability of Ahlfors regular sets

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Length, area, volume, other geometric measure theory (28A75) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (13)

Absolute continuity of the harmonic measure on low dimensional rectifiable sets ⋮ Carleson estimates for the Green function on domains with lower dimensional boundaries ⋮ On the condition for elliptic operators in 1-sided nontangentially accessible domains satisfying the capacity density condition ⋮ Cantor sets with absolutely continuous harmonic measure ⋮ The Green function with pole at infinity applied to the study of the elliptic measure ⋮ Carleson perturbations for the regularity problem ⋮ A Green function characterization of uniformly rectifiable sets of any codimension ⋮ An \(\alpha\)-number characterization of \(L^p\) spaces on uniformly rectifiable sets ⋮ On an obstacle to the converse of Dahlberg's theorem in high codimensions ⋮ Green function estimates on complements of low-dimensional uniformly rectifiable sets ⋮ A new elliptic measure on lower dimensional sets ⋮ Approximation of Green functions and domains with uniformly rectifiable boundaries of all dimensions ⋮ Branch points for (almost-)minimizers of two-phase free boundary problems

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