Concepedia

Harmonic measure on locally flat domains

Duke Mathematical Journal · 1997 · 123 citations · 15 references

Concepts

Spectral TheoryDirichlet FormMean OscillationEngineeringRiemann-hilbert ProblemPotential TheoryTatiana ToroGlobal AnalysisFunctional AnalysisHarmonic SpaceHarmonic Measure

Abstract

We will review work with Tatiana Toro yielding a characterizati on of those domains for which the harmonic measure has a density whose logarithm has vanishing mean oscillation.

References

15

On functions of bounded mean oscillation

Franklin John, Louis Nirenberg · Communications on Pure and Applied Mathematics · 1961 · 1.6K citations

Oscillation Theory, Functional Analysis, Bounded Mean Oscillation +2

Functions of vanishing mean oscillation

Donald Sarason · Transactions of the American Mathematical Society · 1975 · 591 citations

Boundary behavior of harmonic functions in non-tangentially accessible domains

David Jerison, Carlos E. Kenig · Advances in Mathematics · 1982 · 576 citations

Free Boundary Problem, Harmonic Space, Potential Theory +1

Estimates of harmonic measure

Björn E. J. Dahlberg · Archive for Rational Mechanics and Analysis · 1977 · 504 citations

Spectral Theory, Measure Theory, Engineering +4

Solution of the Plateau problem for m-dimensional surfaces of varying topological type

E. R. Reifenberg · Acta Mathematica · 1960 · 369 citations · Full text

M-dimensional Surfaces, Geometric Partial Differential Equation, Geometry +6