\(L^2\)-boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type

DOI10.1007/s00205-023-01852-1OpenAlexW4365514952MaRDI QIDQ2698463

Alejandro Molero, Carmelo Puliatti, Xavier Tolsa, Mihalis Mourgoglou

Publication date: 24 April 2023

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.07332

zbMATH Keywords

second order elliptic equationsrectifiabilityRiesz transformuniform rectifiabilitylayer potentialsDini mean oscillationDavid-Semmes problem

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Second-order elliptic equations (35J15) Length, area, volume, other geometric measure theory (28A75) Spherical harmonics (33C55) Harmonic analysis and PDEs (42B37)

Cites Work

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• Rectifiability of harmonic measure
• Analytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory
• The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions
• On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1
• Spherical harmonics and approximations on the unit sphere. An introduction
• The \(s\)-Riesz transform of an \(s\)-dimensional measure in \(\mathbb R^2\) is unbounded for \(1<s<2\)
• Wavelets and singular integrals on curves and surfaces
• Boundary layer methods for Lipschitz domains in Riemannian manifolds
• Uniform rectifiability from Carleson measure estimates and {\(\epsilon\)}-approximability of bounded harmonic functions
• The Riesz transform and quantitative rectifiability for general Radon measures
• Failure of \(L^2\) boundedness of gradients of single layer potentials for measures with zero low density
• Painlevé's problem and the semiadditivity of analytic capacity.
• The Cauchy integral, analytic capacity, and uniform rectifiability
• \(L^2\)-boundedness of gradients of single-layer potentials and uniform rectifiability
• Gradient of the single layer potential and quantitative rectifiability for general Radon measures
• The two-phase problem for harmonic measure in VMO
• Unboundedness of potential dependent Riesz transforms for totally irregular measures
• Harmonic measure and Riesz transform in uniform and general domains
• Green's function for second order elliptic equations in non-divergence form
• On the \(C^{1}\) regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients
• The Green function estimates for strongly elliptic systems of second order
• Bilipschitz maps, analytic capacity, and the Cauchy integral
• A singular integral approach to a two phase free boundary problem
• An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
• On C¹, C², and weak type-(1,1) estimates for linear elliptic operators
• Layer potential methods for elliptic homogenization problems
• Cauchy integrals on Lipschitz curves and related operators
• Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability
• A two-phase free boundary problem for harmonic measure and uniform rectifiability
• On a two-phase problem for harmonic measure in general domains
• Uniform Rectifiability, Elliptic Measure, Square Functions, and ε-Approximability Via an ACF Monotonicity Formula

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