The regularity problem in domains with lower dimensional boundaries

DOI10.1016/j.jfa.2023.109903OpenAlexW4321793788MaRDI QIDQ2692690

Svitlana Mayboroda, Joseph Feneuil, Zanbing Dai

Publication date: 22 March 2023

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.00628

zbMATH Keywords

degenerate elliptic operatorsDirichlet-regularity problemlow dimensional boundariessquare and non-tangential maximal functions

Mathematics Subject Classification ID

Elliptic equations and elliptic systems (35Jxx) Higher-dimensional potential theory (31Bxx) Harmonic analysis in several variables (42Bxx)

Cites Work

• Unnamed Item
• On a class of non-local operators in conformal geometry
• The \(L^p\) Dirichlet problem for second order elliptic operators and a \(p\)-adapted square function
• The Dirichlet problem in non-smooth domains
• The theory of weights and the Dirichlet problem for elliptic equations
• Estimates of harmonic measure
• The Neumann problem for elliptic equations with non-smooth coefficients
• A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations
• Regularity theory for solutions to second order elliptic operators with complex coefficients and the \(L^{p}\) Dirichlet problem
• Dahlberg's theorem in higher co-dimension
• The Neumann problem for elliptic equations with nonsmooth coefficients. II
• The Dirichlet problem in domains with lower dimensional boundaries
• Uniform rectifiability and elliptic operators satisfying a Carleson measure condition
• 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
• The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients
• Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$
• Semi-Uniform Domains and the A∞ Property for Harmonic Measure
• Elliptic Theory for Sets with Higher Co-dimensional Boundaries
• A change of variable for Dahlberg-Kenig-Pipher operators
• Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition
• An Extension Problem Related to the Fractional Laplacian
• The Dirichlet problem for elliptic equations with drift terms

This page was built for publication: The regularity problem in domains with lower dimensional boundaries