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arXiv · 1811.07713

A sharp Leibniz rule for BV functions in metric spaces

Panu Lahti
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Abstract

We prove a Leibniz rule for 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 BV functions, with quasi semicontinuous test functions.

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Panu Lahti. 2018-11-15. A sharp Leibniz rule for BV functions in metric spaces. https://arxiv.org/abs/1811.07713

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