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arXiv · 1608.01395

Harmonic measure on sets of codimension larger than one

Guy David·Joseph Feneuil·Svitlana Mayboroda
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Abstract

We introduce a new notion of a harmonic measure for a $d$-dimensional set in $\R^n$ with $d<n-1$, that is, when the codimension is strictly bigger than 1. Our measure is associated to a degenerate elliptic PDE, it gives rise to a comprehensive elliptic theory, and, most notably, it is absolutely continuous with respect to the $d$-dimensional Hausdorff measure on reasonably nice sets. This note provides general strokes of the proof of the latter statement for Lipschitz graphs with small Lipschitz constant.

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Guy David, Joseph Feneuil, Svitlana Mayboroda. 2016-08-03. Harmonic measure on sets of codimension larger than one. https://arxiv.org/abs/1608.01395

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