A Green function characterization of uniformly rectifiable sets of any codimension

Joseph Feneuil; Linhan Li

A Green function characterization of uniformly rectifiable sets of any codimension

Joseph Feneuil, Linhan Li

School of Mathematics

Research output: Working paper › Preprint

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
Publisher	ArXiv
Publication status	Published - 27 Feb 2023

Keywords / Materials (for Non-textual outputs)

math.AP
42B37, 35J25, 35J70

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2302.14087v1Submitted manuscript, 483 KB

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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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.

KW - math.AP

KW - 42B37, 35J25, 35J70

M3 - Preprint

BT - A Green function characterization of uniformly rectifiable sets of any codimension

PB - ArXiv

ER -

A Green function characterization of uniformly rectifiable sets of any codimension

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Keywords / Materials (for Non-textual outputs)

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Cite this