Free boundary regularity below the continuous threshold: 2-phase problems

DOI10.1515/CRELLE.2006.050zbMath1106.35147OpenAlexW2042281504MaRDI QIDQ3413776

Carlos E. Kenig, Tatiana Toro

Publication date: 18 December 2006

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2006.050

zbMATH Keywords

regularityharmonic measurePoisson kernelfree boundary problemsboundary regularity problems for harmonic measure and Poisson kernels

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Free boundary problems for PDEs (35R35) Harmonic, subharmonic, superharmonic functions on other spaces (31C05)

Related Items (21)

A free boundary problem for the parabolic Poisson kernel ⋮ Structure of sets which are well approximated by zero sets of harmonic polynomials ⋮ Regularity and free boundary regularity for the $p$-Laplace operator in Reifenberg flat and Ahlfors regular domains ⋮ On a two-phase free boundary condition for \(p\)-harmonic measures ⋮ LOCAL SET APPROXIMATION: MATTILA–VUORINEN TYPE SETS, REIFENBERG TYPE SETS, AND TANGENT SETS ⋮ Two phase free boundary problem for Poisson kernels ⋮ \(p\)-harmonic functions in the Heisenberg group: boundary behaviour in domains well-approximated by non-characteristic hyperplanes ⋮ The two-phase problem for harmonic measure in VMO ⋮ Free boundary regularity for almost-minimizers ⋮ Harmonic polynomials and tangent measures of harmonic measure ⋮ Absolute continuity of harmonic measure for domains with lower regular boundaries ⋮ The Poisson integral formula for variable-coefficient elliptic systems in rough domains ⋮ On an inverse type problem for the heat equation in parabolic regular graph domains ⋮ The one-phase problem for harmonic measure in two-sided NTA domains ⋮ Regularity of the singular set in a two-phase problem for harmonic measure with Hölder data ⋮ Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains ⋮ Tangent measures of elliptic measure and applications ⋮ Stability of Lewis and Vogel's result ⋮ Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions ⋮ Blow-ups of caloric measure in time varying domains and applications to two-phase problems ⋮ A singular integral approach to a two phase free boundary problem

Cites Work

• Unnamed Item
• Unnamed Item
• Harmonic measure and arclength
• A characterization of Poissonian domains
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• On univalent functions, Bloch functions and VMOA
• Harmonic measure on locally flat domains
• Free boundary regularity for harmonic measures and Poisson kernels
• A symmetry theorem revisited
• On functions of bounded mean oscillation
• On the mininum number of domains in which the nodal lines of spherical harmonics divide the sphere

This page was built for publication: Free boundary regularity below the continuous threshold: 2-phase problems