Revista Matemática Iberoamericana


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Volume 31, Issue 2, 2015, pp. 713–752
DOI: 10.4171/RMI/851

Published online: 2015-07-16

The Dirichlet problem with BMO boundary data and almost-real coefficients

Ariel Barton[1]

(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