BMO solvability and \(A_\infty\) condition of the elliptic measures in uniform domains

DOI10.1007/s12220-017-9845-9zbMath1398.35042arXiv1602.00717OpenAlexW3101666583MaRDI QIDQ1651353

Zihui Zhao

Publication date: 12 July 2018

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.00717

zbMATH Keywords

Dirichlet problemelliptic operator in divergence form

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Quasilinear elliptic equations (35J62)

Related Items (14)

Uniform rectifiability implies Varopoulos extensions ⋮ BMO solvability and absolute continuity of caloric measure ⋮ On the condition for elliptic operators in 1-sided nontangentially accessible domains satisfying the capacity density condition ⋮ Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition ⋮ Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition ⋮ Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets ⋮ BMO solvability and absolute continuity of harmonic measure ⋮ Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates ⋮ Boundary rectifiability and elliptic operators with \(W^{1, 1}\) coefficients ⋮ Carleson perturbations of elliptic operators on domains with low dimensional boundaries ⋮ A weak reverse Hölder inequality for caloric measure ⋮ Perturbations of elliptic operators in 1-sided chord-arc domains. Part I: Small and large perturbation for symmetric operators ⋮ Uniform rectifiability and elliptic operators satisfying a Carleson measure condition ⋮ Square function estimates, the BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets

Cites Work

• Unnamed Item
• Unnamed Item
• 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
• Harmonic analysis on chord arc domains
• A new characterization of chord-arc domains
• On the existence of boundary values for harmonic functions in several variables
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• A geometric localization theorem
• The theory of weights and the Dirichlet problem for elliptic equations
• Estimates of harmonic measure
• Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions
• A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations
• Elliptic partial differential equations of second order
• BMO solvability and absolute continuity of harmonic measure
• Uniform rectifiability and harmonic measure. II: Poisson kernels in \(L^p\) imply uniform rectifiability
• \(A_\infty\) implies NTA for a class of variable coefficient elliptic operators
• BMO solvability and the \(A_{\infty}\) condition for elliptic operators
• \(H^p\) spaces of several variables
• Square functions and the \(A_\infty\) property of elliptic measures
• Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$
• A Criterion for the Absolute Continuity of the Harmonic Measure Associated With an Elliptic Operator
• On Strong Barriers and an Inequality of Hardy for Domains in R ⁿ
• On the Absolute Continuity of Elliptic Measures
• Another Characterization of BMO
• Dirichlet Problem in Lipschitz Domains with BMO Data
• POTENTIAL-THEORETIC CHARACTERIZATIONS OF NONSMOOTH DOMAINS
• Positive Harmonic Functions on Lipschitz Domains
• Boundary Harnack principle and Martin boundary for a uniform domain

This page was built for publication: BMO solvability and \(A_\infty\) condition of the elliptic measures in uniform domains