Abstract
We introduce a new notion of a harmonic measure for a d-dimensional set in Rn with d<n−1, that is, when the codimension is strictly bigger than 1. Our measure is associated with 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.
Original language | English (US) |
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Pages (from-to) | 406-410 |
Number of pages | 5 |
Journal | Comptes Rendus Mathematique |
Volume | 355 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2017 |
Bibliographical note
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