Revista Matemática Iberoamericana
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Published online: 2015-07-16
The Dirichlet problem with BMO boundary data and almost-real coefficientsAriel Barton (1) University of Missouri, Columbia, USA
It is known that a function, harmonic in a Lipschitz domain, is the Poisson extension of a BMO function if and only if its gradient satisfies a Carleson-measure condition. We show that the same is true of functions that satisfy elliptic equations in two-dimensional Lipschitz domains, provided the coefficients are independent of one coordinate and have small imaginary part.
Keywords: Elliptic equations, Dirichlet problem, Lipschitz domains, Carleson measures, bounded mean oscillation, layer potentials
Barton Ariel: The Dirichlet problem with BMO boundary data and almost-real coefficients. Rev. Mat. Iberoamericana 31 (2015), 713-752. doi: 10.4171/RMI/851