A new elliptic measure on lower dimensional sets

DOI10.1007/s10114-019-9001-5zbMath1414.28008arXiv1807.07035OpenAlexW2963896473WikidataQ127817654 ScholiaQ127817654MaRDI QIDQ2311722

Guy David, Joseph Feneuil, Svitlana Mayboroda

Publication date: 4 July 2019

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.07035

zbMATH Keywords

absolute continuitydegenerate elliptic operatorsDahlberg's theoremDirichlet solvability.elliptic measure in higher codimension

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Length, area, volume, other geometric measure theory (28A75) Hausdorff and packing measures (28A78) Harmonic analysis and PDEs (42B37)

Related Items (7)

Absolute continuity of the harmonic measure on low dimensional rectifiable sets ⋮ Carleson estimates for the Green function on domains with lower dimensional boundaries ⋮ A change of variable for Dahlberg-Kenig-Pipher operators ⋮ The Green function with pole at infinity applied to the study of the elliptic measure ⋮ Green function estimates on complements of low-dimensional uniformly rectifiable sets ⋮ Carleson perturbations of elliptic operators on domains with low dimensional boundaries ⋮ Traces on General Sets in ${R}^n$ for Functions with no Differentiability Requirements

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions
• On the dimension of \(p\)-harmonic measure in space
• On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1
• A new characterization of chord-arc domains
• The one-phase problem for harmonic measure in two-sided NTA domains
• Harmonic measure and arclength
• Morceaux de graphes lipschitziens et intégrales singulières sur une surface
• The \(L^p\) Dirichlet problem for second order elliptic operators and a \(p\)-adapted square function
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• The Dirichlet problem in non-smooth domains
• The Green function for uniformly elliptic equations
• The Wiener test for degenerate elliptic equations
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Estimates of harmonic measure
• A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations
• Elliptic partial differential equations of second order
• Regularity theory for solutions to second order elliptic operators with complex coefficients and the \(L^{p}\) Dirichlet problem
• Quasi-linear PDEs and low-dimensional sets
• Uniform rectifiability from Carleson measure estimates and {\(\epsilon\)}-approximability of bounded harmonic functions
• BMO solvability and the \(A_\infty\) condition for second order parabolic operators
• Dahlberg's theorem in higher co-dimension
• Lipschitz and bi-Lipschitz functions
• Construction of a singular elliptic-harmonic measure
• The Cauchy integral, analytic capacity, and uniform rectifiability
• The Dirichlet problem in domains with lower dimensional boundaries
• Square functions, nontangential limits, and harmonic measure in codimension larger than 1
• Convexity of power functions and bilinear embedding for divergence-form operators with complex coefficients
• Square function estimates, the BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets
• BMO solvability and the \(A_{\infty}\) condition for elliptic operators
• The Green function estimates for strongly elliptic systems of second order
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• Criterion for the \(L^p\)-dissipativity of second order differential operators with complex coefficients
• Square functions and the \(A_\infty\) property of elliptic measures
• Reifenberg parameterizations for sets with holes
• Semi-Uniform Domains and the A∞ Property for Harmonic Measure
• Uniform rectifiability, Calderón-Zygmund operators with odd kernel, and quasiorthogonality
• Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains
• Opérateurs d'intégrale singulière sur les surfaces régulières
• The local regularity of solutions of degenerate elliptic equations
• Sobolev met Poincaré
• Characterization of Subsets of Rectifiable Curves in R ⁿ
• Elliptic Theory for Sets with Higher Co-dimensional Boundaries
• Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators
• The Dirichlet problem for elliptic equations with drift terms

This page was built for publication: A new elliptic measure on lower dimensional sets