Approximation of Green functions and domains with uniformly rectifiable boundaries of all dimensions

DOI10.1016/j.aim.2022.108717zbMath1503.35085arXiv2010.09793OpenAlexW3093654348MaRDI QIDQ2094599

Guy David, Svitlana Mayboroda

Publication date: 8 November 2022

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.09793

zbMATH Keywords

elliptic operatorsGreen functionuniform rectifiability

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Green's functions for elliptic equations (35J08)

Related Items (4)

Cantor sets with absolutely continuous harmonic measure ⋮ The Green function with pole at infinity applied to the study of the elliptic measure ⋮ A Green function characterization of uniformly rectifiable sets of any codimension ⋮ On an obstacle to the converse of Dahlberg's theorem in high codimensions

Cites Work

• The weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability
• Harmonic measure on sets of codimension larger than one
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Uniform rectifiability from Carleson measure estimates and {\(\epsilon\)}-approximability of bounded harmonic functions
• Dahlberg's theorem in higher co-dimension
• Singular sets of minimizers for the Mumford-Shah functional
• Construction of a singular elliptic-harmonic measure
• Uniform rectifiability and harmonic measure. II: Poisson kernels in \(L^p\) imply uniform rectifiability
• Square functions, nontangential limits, and harmonic measure in codimension larger than 1
• Uniform rectifiability and elliptic operators satisfying a Carleson measure condition
• Carleson measure estimates for the Green function
• Absolute continuity of the harmonic measure on low dimensional rectifiable sets
• Harmonic measure and quantitative connectivity: geometric characterization of the \(L^p\)-solvability of the Dirichlet problem
• \(A_\infty\) implies NTA for a class of variable coefficient elliptic operators
• Uniform rectifiability, Calderón-Zygmund operators with odd kernel, and quasiorthogonality
• A Criterion for the Boundedness of Singular Integrals on Hypersurfaces
• Elliptic Theory for Sets with Higher Co-dimensional Boundaries
• Elliptic theory in domains with boundaries of mixed dimension
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