A Green function characterization of uniformly rectifiable sets of any codimension
Abstract
In this paper, we obtain a unified characterization of uniformly rectifiable sets of any codimension in terms of a Carleson estimate on the second derivatives of the Green function. When restricted to domains with boundaries of codimension 1, our result generalizes a previous result of Azzam for the Laplacian to more general elliptic operators. For domains with boundaries of codimension greater than 1, our result is completely new.
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