JournalsrmiVol. 31, No. 2pp. 713–752

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

  • Ariel Barton

    University of Missouri, Columbia, USA
The Dirichlet problem with BMO boundary data and almost-real coefficients cover
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Abstract

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. 713–752

DOI 10.4171/RMI/851