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.
Cite this article
Ariel Barton, The Dirichlet problem with BMO boundary data and almost-real coefficients. Rev. Mat. Iberoam. 31 (2015), no. 2, pp. 713–752DOI 10.4171/RMI/851