6533b7d9fe1ef96bd126c416

RESEARCH PRODUCT

Characterisation of upper gradients on the weighted Euclidean space and applications

Enrico PasqualettoTapio RajalaDanka Lučić

subject

Pure mathematicsEuclidean spaceApplied MathematicsMathematics::Analysis of PDEsContext (language use)Sobolev spaceLipschitz continuityFunctional Analysis (math.FA)46E35 53C23 26B05differentiaaligeometriaSobolev spaceMathematics - Functional AnalysisMathematics - Analysis of PDEsRadon measureEuclidean geometryFOS: MathematicsWeighted Euclidean spaceDecomposability bundlefunktionaalianalyysiEquivalence (measure theory)MathematicsAnalysis of PDEs (math.AP)

description

In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all Lipschitz functions.

yearjournalcountryeditionlanguage
2020-07-23
https://dx.doi.org/10.48550/arxiv.2007.11904