A singular integral approach to a two phase free boundary problem

DOI10.1090/proc/13035zbMath1361.42012arXiv1505.05419OpenAlexW2216506392MaRDI QIDQ2814415

Simon Bortz, Steven Hofmann

Publication date: 22 June 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.05419

zbMATH Keywords

singular integralsfree boundary problemsVMOuniform rectifiabilitylayer potentialsPoisson kernelschord-arc domainsNTA domainsAhlfors-David regular

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Free boundary problems for PDEs (35R35) Boundary behavior of harmonic functions in higher dimensions (31B25) Green's functions for elliptic equations (35J08) Harmonic analysis and PDEs (42B37)

Related Items (6)

Structure of sets which are well approximated by zero sets of harmonic polynomials ⋮ Two phase free boundary problem for Poisson kernels ⋮ The two-phase problem for harmonic measure in VMO ⋮ Small-constant uniform rectifiability ⋮ \(L^2\)-boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type ⋮ The one-phase problem for harmonic measure in two-sided NTA domains

Cites Work

• On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Harmonic measure on locally flat domains
• On the Hausdorff dimension of harmonic measure in higher dimension
• The Cauchy integral, analytic capacity, and uniform rectifiability
• Free boundary regularity for harmonic measures and Poisson kernels
• Regularity of the Poisson kernel and free boundary problems
• Free boundary regularity below the continuous threshold: 2-phase problems
• Poisson kernel characterization of Reifenberg flat chord arc domains
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A singular integral approach to a two phase free boundary problem