6533b7cefe1ef96bd1257b50
RESEARCH PRODUCT
A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space
Enrico PasqualettoDanka LučićSimone Di Marinosubject
Mathematics::Functional AnalysisPure mathematicsLebesgue measureEuclidean spaceGeneral Mathematics010102 general mathematicsAbsolute continuity01 natural sciencesMeasure (mathematics)Functional Analysis (math.FA)Mathematics - Functional AnalysisdifferentiaaligeometriaEuclidean distanceSobolev spaceNorm (mathematics)0103 physical sciencesRadon measureFOS: Mathematics010307 mathematical physics0101 mathematicsfunktionaalianalyysi53C23 46E35 26B05Mathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-05-06 | Comptes Rendus. Mathématique |