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arXiv · 1511.04503

Trace and extension theorems for functions of bounded variation

Lukáš Malý·Nageswari Shanmugalingam·Marie Snipes
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Abstract

In this paper we show that every $L^1$-integrable function on $\partial\Omega$ can be obtained as the trace of a function of bounded variation in $\Omega$ whenever $\Omega$ is a domain with regular boundary $\partial\Omega$ in a doubling metric measure space. In particular, the trace class of $BV(\Omega)$ is $L^1(\partial\Omega)$ provided that $\Omega$ supports a 1-Poincar\'e inequality. We also construct a bounded linear extension from a Besov class of functions on $\partial\Omega$ to $BV(\Omega)$.

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Lukáš Malý, Nageswari Shanmugalingam, Marie Snipes. 2015-11-14. Trace and extension theorems for functions of bounded variation. https://arxiv.org/abs/1511.04503

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