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

School of Mathematics

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Abstract / Description of output

In this paper, we obtain a unified characterization of uniformly rectifiable sets of {\it 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.

Original language	English
Article number	109220
Journal	Advances in Mathematics
Volume	430
Early online date	28 Jul 2023
DOIs	https://doi.org/10.1016/j.aim.2023.109220
Publication status	Published - 1 Oct 2023

Keywords / Materials (for Non-textual outputs)

math.AP
42B37, 35J25, 35J70

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10.1016/j.aim.2023.109220Licence: Creative Commons: Attribution (CC-BY)

https://arxiv.org/abs/2302.14087

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title = "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 {\it 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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AU - Li, Linhan

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N2 - In this paper, we obtain a unified characterization of uniformly rectifiable sets of {\it 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.

AB - In this paper, we obtain a unified characterization of uniformly rectifiable sets of {\it 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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KW - 42B37, 35J25, 35J70

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M3 - Article

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JO - Advances in Mathematics

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A Green function characterization of uniformly rectifiable sets of any codimension

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