Quantitative absolute continuity of harmonic measure and the Dirichlet problem: a survey of recent progress
DOI10.1007/s10114-019-8444-zzbMath1421.31010OpenAlexW2945994027MaRDI QIDQ2311726
Publication date: 4 July 2019
Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10114-019-8444-z
Boundary value problems for second-order elliptic equations (35J25) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Boundary behavior of harmonic functions in higher dimensions (31B25) Research exposition (monographs, survey articles) pertaining to potential theory (31-02) Harmonic analysis and PDEs (42B37)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Rectifiability of harmonic measure
- Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions
- On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1
- The weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability
- The one-phase problem for harmonic measure in two-sided NTA domains
- Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited
- Quantitative Fatou theorems and uniform rectifiability
- Harmonic measure and arclength
- Morceaux de graphes lipschitziens et intégrales singulières sur une surface
- Doubling conditions for harmonic measure in John domains
- Boundary behavior of harmonic functions in non-tangentially accessible domains
- Estimates of harmonic measure
- Uniform rectifiability from Carleson measure estimates and {\(\epsilon\)}-approximability of bounded harmonic functions
- BMO solvability and absolute continuity of harmonic measure
- Absolute continuity of harmonic measure for domains with lower regular boundaries
- Rectifiability, interior approximation and harmonic measure
- On the Hausdorff dimension of harmonic measure in higher dimension
- The Cauchy integral, analytic capacity, and uniform rectifiability
- Harmonic measure and Riesz transform in uniform and general domains
- \(A_\infty\) implies NTA for a class of variable coefficient elliptic operators
- Symmetry theorems and uniform rectifiability
- Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$
- Regularity of the Poisson kernel and free boundary problems
- Semi-Uniform Domains and the A∞ Property for Harmonic Measure
- A Criterion for the Boundedness of Singular Integrals on Hypersurfaces
- Weighted norm inequalities for maximal functions and singular integrals
- Variational problems with two phases and their free boundaries
- Poisson kernel characterization of Reifenberg flat chord arc domains
- Singular Sets for Harmonic Measure on Locally Flat Domains with Locally Finite Surface Measure
- On weak reverse hölder inequalities for nondoubling harmonic measures
- A T(b) theorem with remarks on analytic capacity and the Cauchy integral
- POTENTIAL-THEORETIC CHARACTERIZATIONS OF NONSMOOTH DOMAINS
- Boundary problems in the theory of univalent functions
- Weighted Norm Inequalities for the Hardy Maximal Function
- Boundary Harnack principle and Martin boundary for a uniform domain
- Uniform Rectifiability, Elliptic Measure, Square Functions, and ε-Approximability Via an ACF Monotonicity Formula
This page was built for publication: Quantitative absolute continuity of harmonic measure and the Dirichlet problem: a survey of recent progress