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.
Sobolev and BV spaces on metric measure spaces via derivations and integration by parts
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abstract
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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UNVERDICTED 2representative citing papers
A sufficient condition on a unital algebra of locally Lipschitz functions makes the energy-approximation BV space coincide with the standard metric BV space.
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Indecomposable sets of finite perimeter in doubling metric measure spaces
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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Functions of bounded variation and Lipschitz algebras in metric measure spaces
A sufficient condition on a unital algebra of locally Lipschitz functions makes the energy-approximation BV space coincide with the standard metric BV space.