Dahlberg's theorem in higher co-dimension

DOI10.1016/j.jfa.2019.02.006zbMath1414.42032arXiv1704.00667OpenAlexW2963583230WikidataQ128378344 ScholiaQ128378344MaRDI QIDQ1731875

Joseph Feneuil, Guy David, Svitlana Mayboroda

Publication date: 14 March 2019

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

Full work available at URL: https://arxiv.org/abs/1704.00667

zbMATH Keywords

harmonic measuredegenerate elliptic equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Degenerate elliptic equations (35J70) Harmonic analysis and PDEs (42B37)

Related Items (22)

Generalized Carleson perturbations of elliptic operators and applications ⋮ Regularity theory for solutions to second order elliptic operators with complex coefficients and the \(L^{p}\) Dirichlet problem ⋮ 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 ⋮ On the condition for elliptic operators in 1-sided nontangentially accessible domains satisfying the capacity density condition ⋮ Small 𝐴_{∞} results for Dahlberg-Kenig-Pipher operators in sets with uniformly rectifiable boundaries ⋮ 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 ⋮ On an obstacle to the converse of Dahlberg's theorem in high codimensions ⋮ Small-constant uniform rectifiability ⋮ The regularity problem in domains with lower dimensional boundaries ⋮ Green function estimates on complements of low-dimensional uniformly rectifiable sets ⋮ Carleson perturbations of elliptic operators on domains with low dimensional boundaries ⋮ Good elliptic operators on Cantor sets ⋮ The Dirichlet problem in domains with lower dimensional boundaries ⋮ Square functions, nontangential limits, and harmonic measure in codimension larger than 1 ⋮ A new elliptic measure on lower dimensional sets ⋮ Square function estimates, the BMO Dirichlet problem, and absolute continuity of harmonic 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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rectifiability of harmonic measure
• 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 weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability
• Harmonic measure on sets of codimension larger than one
• Harmonic measure and arclength
• Morceaux de graphes lipschitziens et intégrales singulières sur une surface
• On singularity of harmonic measure in space
• Hausdorff dimension of harmonic measures in the plane
• The Dirichlet problem in non-smooth domains
• The Wiener test for degenerate elliptic equations
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• The theory of weights and the Dirichlet problem for elliptic equations
• Some remarks on harmonic measure in space
• Estimates of harmonic measure
• A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations
• Quasi-linear PDEs and low-dimensional sets
• BMO solvability and the \(A_\infty\) condition for second order parabolic operators
• An analyst's traveling salesman theorem for sets of dimension larger than one
• Geometric conditions and existence of bi-Lipschitz parameterizations
• On the Hausdorff dimension of harmonic measure in higher dimension
• Calderon-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderon
• The solution of the Kato square root problem for second order elliptic operators on \(\mathbb R^n\).
• Geometric measure theory.
• The Cauchy integral, analytic capacity, and uniform rectifiability
• Uniform rectifiability and harmonic measure. II: Poisson kernels in \(L^p\) imply uniform rectifiability
• On the distortion of sets on a Jordan curve under conformal mapping
• Square functions and the \(A_\infty\) property of elliptic measures
• Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$
• Reifenberg parameterizations for sets with holes
• Uniform rectifiability, Calderón-Zygmund operators with odd kernel, and quasiorthogonality
• On the Distortion of Boundary Sets Under Conformal Mappings
• A Characterization of Potential Spaces
• The local regularity of solutions of degenerate elliptic equations
• Weighted norm inequalities for maximal functions and singular integrals
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• Elliptic Theory for Sets with Higher Co-dimensional Boundaries
• 𝐿^{𝑝}-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets
• Boundary problems in the theory of univalent functions
• An Extension Problem Related to the Fractional Laplacian
• 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
• Kähler-Einstein metrics with edge singularities

This page was built for publication: Dahlberg's theorem in higher co-dimension