Harmonic measure and quantitative connectivity: geometric characterization of the L^p-solvability of the Dirichlet problem

2020/07/20 by Jonas Azzam, Steve Hofmann, José María Martell +2 · 9 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research

paper · pdf · doi:10.1007/s00222-020-00984-5

Citations

• Variational problems with two phases and their free boundaries

Cited by

• The regularity problem in domains with lower dimensional boundaries
• Green functions and smooth distances
• Interactions between Quantitative Rectifiability, Singular Integrals, and Boundary Value Problems for Harmonic Functions
• Carleson perturbations of locally Lipschitz elliptic operators
• An alternative proof of the L^p-regularity problem for Dahlberg-Kenig-Pipher operators on \mathbb Rⁿ₊
• Square functions, non-tangential limits and harmonic measure in\n co-dimensions larger than one
• Robin Problems of Elliptic Equations on Rough Domains: Hölder Regularity, Green's Functions, and Harmonic Measures
• Boundary Value Problems in graph Lipschitz domains in the plane with A_∞-measures on the boundary
• Green functions and smooth distances. [europepmc]
• On the Regularity Problem for Parabolic Operators and the Role of Half-Time Derivative. [europepmc]