A note on BV and 1-Sobolev functions on the weighted Euclidean space

A note on BV and 1-Sobolev functions on the weighted Euclidean space

In the setting of the Euclidean space equipped with an arbitrary Radon measure, we prove the equivalence between several notions of function of bounded variation present in the literature. We also study the relation between various definitions of 1-Sobolev function.

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Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2021-10
Hauptverfasser: Gelli, Maria Stella, Lučić, Danka
Format: Artikel
Sprache:eng
Schlagworte:
Euclidean geometry
Euclidean space
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Zusammenfassung:In the setting of the Euclidean space equipped with an arbitrary Radon measure, we prove the equivalence between several notions of function of bounded variation present in the literature. We also study the relation between various definitions of 1-Sobolev function.
ISSN:2331-8422