Square function estimates, the BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets
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Publication:2326560
DOI10.2140/apde.2019.12.1843zbMath1432.35074arXiv1802.09648OpenAlexW3101161138MaRDI QIDQ2326560
Svitlana Mayboroda, Zihui Zhao
Publication date: 10 October 2019
Published in: Analysis \& PDE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1802.09648
Boundary value problems for second-order elliptic equations (35J25) Connections of harmonic functions with differential equations in higher dimensions (31B35) Harmonic analysis and PDEs (42B37)
Related Items (9)
Absolute continuity of the harmonic measure on low dimensional rectifiable sets ⋮ 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 ⋮ Carleson perturbations of elliptic operators on domains with low dimensional boundaries ⋮ 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 ⋮ Traces on General Sets in ${R}^n$ for Functions with no Differentiability Requirements
Cites Work
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- Rectifiability of harmonic measure
- Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions
- Harmonic analysis on chord arc domains
- A new characterization of chord-arc domains
- The weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability
- Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited
- Area integral estimates for elliptic differential operators with non- smooth coefficients
- Harmonic measure and arclength
- Boundary behavior of harmonic functions in non-tangentially accessible domains
- Some new function spaces and their applications to harmonic analysis.
- Estimates of harmonic measure
- Uniform rectifiability from Carleson measure estimates and {\(\epsilon\)}-approximability of bounded harmonic functions
- BMO solvability and \(A_\infty\) condition of the elliptic measures in uniform domains
- Dahlberg's theorem in higher co-dimension
- Uniform rectifiability and harmonic measure. II: Poisson kernels in \(L^p\) imply uniform rectifiability
- Boundary rectifiability and elliptic operators with \(W^{1, 1}\) coefficients
- Harmonic measure and Riesz transform in uniform and general domains
- \(A_\infty\) implies NTA for a class of variable coefficient elliptic operators
- BMO solvability and the \(A_{\infty}\) condition for elliptic operators
- On functions of bounded mean oscillation
- Extensions of Hardy spaces and their use in analysis
- On weak reverse hölder inequalities for nondoubling harmonic measures
- A T(b) theorem with remarks on analytic capacity and the Cauchy integral
- Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries
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