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

Ariel Barton | Zendy

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

Author(s) -

Ariel Barton

Publication year - 2015

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/851

Subject(s) - lipschitz continuity , mathematics , lipschitz domain , mathematical analysis , harmonic function , bounded mean oscillation , dirichlet problem , function (biology) , domain (mathematical analysis) , harmonic measure , boundary (topology) , extension (predicate logic) , poisson's equation , measure (data warehouse) , dirichlet distribution , poisson kernel , poisson distribution , pure mathematics , boundary value problem , bounded function , statistics , database , evolutionary biology , computer science , programming language , biology

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.

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