Harmonic Measure Is Absolutely Continuous with Respect to the Hausdorff Measure on All Low-Dimensional Uniformly Rectifiable Sets

DOI10.1093/IMRN/RNAC109zbMath1527.35149arXiv2006.14661MaRDI QIDQ6155928

Svitlana Mayboroda, Guy David

Publication date: 7 June 2023

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.14661

zbMATH Keywords

degenerate elliptic operatorelliptic measuredomain with uniformly rectifiable boundary

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Degenerate elliptic equations (35J70) Boundary behavior of harmonic functions in higher dimensions (31B25) Harmonic analysis and PDEs (42B37)

Related Items (9)

On the condition for elliptic operators in 1-sided nontangentially accessible domains satisfying the capacity density condition ⋮ 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 ⋮ Carleson perturbations of elliptic operators on domains with low dimensional boundaries ⋮ Good elliptic operators on Cantor sets ⋮ Square functions, nontangential limits, and harmonic measure in codimension larger than 1

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