Harmonic analysis on chord arc domains

DOI10.1007/s12220-012-9322-4zbMath1282.35151arXiv1101.0331OpenAlexW2079509348MaRDI QIDQ375742

Jill Pipher, Emmanouil Milakis, Tatiana Toro

Publication date: 31 October 2013

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

Full work available at URL: https://arxiv.org/abs/1101.0331

zbMATH Keywords

tent spaceschord arc domainsDirichlet problem for second order divergence form elliptic operatorselliptic measuresperturbations of the Laplacian

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Boundary value problems for second-order elliptic equations (35J25) Perturbations in context of PDEs (35B20) Connections of harmonic functions with differential equations in higher dimensions (31B35)

Related Items (13)

BMO solvability and \(A_\infty\) condition of the elliptic measures in uniform domains ⋮ 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 ⋮ Small-constant uniform rectifiability ⋮ 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 ⋮ Perturbations of elliptic operators in 1-sided chord-arc domains. Part I: Small and large perturbation for symmetric operators ⋮ Perturbation theory for solutions to second order elliptic operators with complex coefficients and the \(L^p\) Dirichlet problem ⋮ 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

Cites Work

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• A Criterion for the Absolute Continuity of the Harmonic Measure Associated With an Elliptic Operator
• On the Absolute Continuity of Elliptic Measures
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral

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