Publications
2002
Issue 29

MiS Preprint Repository

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MiS Preprint

29/2002

Stationary measures and rectifiability

Roger Moser

Abstract

For integers $1 \leq p < n$ , we consider $R^{n \times n}$ -valued Radon measures $μ = (μ_{α β})$ on an open set $Ω \subset R^{n}$ which satisfy $\int_{Ω} (d i v ϕ d μ_{α α} - p \frac{\partial ϕ^{α}}{\partial x^{β}} d μ_{α β}) = 0$ for all $ϕ \in C_{0}^{1} (Ω, R^{n})$ . We show that under certain conditions, $μ$ has an $(n - p)$ -dimensional density everywhere, and the set of points of positive density is countably $(n - p)$ -rectifiable. This simplifies the proofs of several rectifiability theorems involving varifolds with vanishing first variations, $p$ -harmonic maps, or Yang-Mills connections.

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Received:: 21.03.02

Published:: 21.03.02

MSC Codes:: 49Q15, 49Q05, 58E20, 58E15

Keywords:: rectifiability, minimal varifolds, p-harmonic maps, yang-mills connections

Related publications

inJournal

2003 Repository Open Access

Roger Moser

Stationary measures and rectifiability

In: Calculus of variations and partial differential equations, 17 (2003) 4, pp. 357-368

BibTex DOI: 10.1007/s00526-002-0173-x