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A sharp Leibniz rule for \({\mathrm {BV}}\) functions in metric spaces

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Abstract

We prove a Leibniz rule for \({\mathrm {BV}}\) functions in a complete metric space that is equipped with a doubling measure and supports a Poincaré inequality. Unlike in previous versions of the rule, we do not assume the functions to be locally essentially bounded and the end result does not involve a constant \(C\ge 1\), and so our result seems to be essentially the best possible. In order to obtain the rule in such generality, we first study the weak* convergence of the variation measure of \({\mathrm {BV}}\) functions, with quasi semicontinuous test functions.

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  1. Institut für Mathematik, Universität Augsburg, Universitätsstr. 14, 86159, Augsburg, Germany

    Panu Lahti

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Lahti, P. A sharp Leibniz rule for \({\mathrm {BV}}\) functions in metric spaces. Rev Mat Complut 33, 797–816 (2020). https://doi.org/10.1007/s13163-019-00341-y

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