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.
Characterisation of upper gradients on the weighted Euclidean space and applications / Lucic, Danka; Pasqualetto, Enrico; Rajala, Tapio. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 200:6(2021), pp. 2473-2513. [10.1007/s10231-021-01088-4]
Characterisation of upper gradients on the weighted Euclidean space and applications
Lucic, Danka;Pasqualetto, Enrico;
2021-01-01
Abstract
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.File in questo prodotto:
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