A Green function characterization of uniformly rectifiable sets of any codimension

2023/07/28 by Joseph Feneuil, Linhan Li · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Differential Equations and Boundary Problems

paper · doi:10.1016/j.aim.2023.109220

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.

Cited by

• Carleson perturbations of locally Lipschitz elliptic operators

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