A Green function characterization of uniformly rectifiable sets of any codimension

Joseph Feneuil,Linhan Li

doi:10.1016/j.aim.2023.109220

A Green function characterization of uniformly rectifiable sets of any codimension

Joseph Feneuil, Linhan Li

Open Access

https://doi.org/10.1016/j.aim.2023.109220

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Journal: Advances in Mathematics	Publication Date: Jul 28, 2023
License type: cc-by

Affiliation: Australian Mathematical Sciences Institute, Australian National University, University of Edinburgh

#General Elliptic Operators #Green Function + Show 5 more

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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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