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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Bibliographic Details
Published inAtti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni Vol. 33; no. 4; pp. 757 - 794
Main Authors Gelli, Maria Stella, Lučić, Danka
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 03.02.2023
Subjects
Euclidean geometry
Functions of bounded variation
Geometry, Plane
Geometry, Solid
Tests, problems and exercises
Weighting (Statistics)
Italy
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Summary: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:1120-6330
1720-0768
DOI:10.4171/rlm/988