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arxiv: 1409.5620 · v1 · pith:4XHQP6VBnew · submitted 2014-09-19 · 🧮 math.MG · math.FA

Sobolev and BV spaces on metric measure spaces via derivations and integration by parts

Simone Di Marino This is my paper
classification 🧮 math.MG math.FA
keywords spacesmetricderivationsintegrationpartssobolevabstractdefinition
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We develop a theory of BV and Sobolev Spaces via integration by parts formula in abstract metric spaces; the role of vector fields is played by Weaver's metric derivations. The definition hereby given is shown to be equivalent to many others present in literature.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    Decomposition theorem into indecomposable sets of finite perimeter plus characterization of extreme BV points, both requiring isotropicity, in doubling metric measure spaces with weak (1,1)-Poincaré inequality.

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    A sufficient condition on a unital algebra of locally Lipschitz functions makes the energy-approximation BV space coincide with the standard metric BV space.