Non-rigidity of the absolutely continuous part of A-free measures

2023/12/10 by Luigi De Masi, De Masi, Luigi, Carlo Gasparetto +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2312.06026

openalex publication_date 2023/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We generalize a result by Alberti, showing that, if a first-order linear differential operator A belongs to a certain class, then any L¹ function is the absolutely continuous part of a measure μ satisfying Aμ=0. When A is scalar valued, we provide a necessary and sufficient condition for the above property to hold true and we prove dimensional estimates on the singular part of μ. Finally, we show that operators in the above class satisfy a Lusin-type property.

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