\(A_\infty\) implies NTA for a class of variable coefficient elliptic operators

DOI10.1016/j.jde.2017.06.028zbMath1378.35092arXiv1611.09561OpenAlexW2558469179MaRDI QIDQ2404253

Tatiana Toro, Steven Hofmann, José Maria Martell

Publication date: 18 September 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.09561

zbMATH Keywords

Ahlfors regular boundaryelliptic measuredivergence form elliptic operator

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Green's functions for elliptic equations (35J08)

Related Items (23)

Regularity theory for solutions to second order elliptic operators with complex coefficients and the \(L^{p}\) Dirichlet problem ⋮ BMO solvability and \(A_\infty\) condition of the elliptic measures in uniform domains ⋮ Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries ⋮ 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 ⋮ Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition ⋮ A Green function characterization of uniformly rectifiable sets of any codimension ⋮ Optimal Poisson kernel regularity for elliptic operators with Hölder continuous coefficients in vanishing chord-arc domains ⋮ A two-phase free boundary problem for harmonic measure and uniform rectifiability ⋮ Green function estimates on complements of low-dimensional uniformly rectifiable sets ⋮ Elliptic measures for Dahlberg-Kenig-Pipher operators: asymptotically optimal estimates ⋮ 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 ⋮ Perturbations of elliptic operators in 1-sided chord-arc domains. Part I: Small and large perturbation for symmetric operators ⋮ Tangent measures of elliptic measure and applications ⋮ \(L^2\)-boundedness of gradients of single-layer potentials and uniform rectifiability ⋮ Uniform rectifiability and elliptic operators satisfying a Carleson measure condition ⋮ Quantitative absolute continuity of harmonic measure and the Dirichlet problem: a survey of recent progress ⋮ Elliptic measures and square function estimates on 1-sided chord-arc domains ⋮ Square function estimates, the BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets ⋮ Extrapolation of the Dirichlet problem for elliptic equations with complex coefficients ⋮ Approximation of Green functions and domains with uniformly rectifiable boundaries of all dimensions ⋮ Carleson measure estimates for the Green function

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