A1 Journal article (refereed)
A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space (2020)
Une preuve courte de la Hilbertianité infinitésimale de l’espace euclidien à poids
Di Marino, S., Lučić, D., & Pasqualetto, E. (2020). A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space. Comptes Rendus Mathematique, 358(7), 817-825. https://doi.org/10.5802/crmath.88
JYU authors or editors
Publication details
All authors or editors: Di Marino, Simone; Lučić, Danka; Pasqualetto, Enrico
Journal or series: Comptes Rendus Mathematique
ISSN: 1631-073X
eISSN: 1778-3569
Publication year: 2020
Volume: 358
Issue number: 7
Pages range: 817-825
Publisher: Institut de France
Publication country: France
Publication language: English
DOI: https://doi.org/10.5802/crmath.88
Publication open access: Openly available
Publication channel open access: Open Access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/73342
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2005.02924
Abstract
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of the Alberti–Marchese decomposability bundle. As a consequence of our arguments, we also prove that if the Sobolev norm is closable on compactly-supported smooth functions, then the reference measure is absolutely continuous with respect to the Lebesgue measure.
Keywords: differential geometry; functional analysis
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Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 1