Characterisation of upper gradients on the weighted Euclidean space and applications
Lučić, D., Pasqualetto, E., & Rajala, T. (2021). Characterisation of upper gradients on the weighted Euclidean space and applications. Annali di Matematica Pura ed Applicata, 200(6), 2473-2513. https://doi.org/10.1007/s10231-021-01088-4
Published inAnnali di Matematica Pura ed Applicata
DisciplineAnalyysin ja dynamiikan tutkimuksen huippuyksikköMatematiikkaAnalysis and Dynamics Research (Centre of Excellence)Mathematics
© 2021 the Authors
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.
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Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF
Additional information about fundingAll authors are partially supported by the Academy of Finland, Project 314789.
Showing items with similar title or keywords.
Di Marino, Simone; Lučić, Danka; Pasqualetto, Enrico (Institut de France, 2020)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 ...
Le Donne, Enrico; Lučić, Danka; Pasqualetto, Enrico (Springer, 2022)We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations ...
Pasqualetto, Enrico (Institute of Mathematics, Polish Academy of Sciences, 2022)We prove that on an arbitrary metric measure space the following property holds: a single test plan can be used to recover the minimal weak upper gradient of any Sobolev function. This means that, in order to identify which ...
Lučić, Danka; Pasqualetto, Enrico (Canadian Mathematical Society, 2020)The main result of this paper is the following: any weighted Riemannian manifold (M,g,𝜇), i.e., a Riemannian manifold (M,g) endowed with a generic non-negative Radon measure 𝜇, is infinitesimally Hilbertian, which ...
Zhang, Yi (University of Jyväskylä, 2017)This doctoral thesis deals with geometric characterizations of bounded planar simply connected Sobolev extension domains. It consists of three papers. In the ﬁrst and third papers we give full geometric characterizations ...