Abstract
We prove a lower semicontinuity result for a functional of linear growth initially defined by
for \(u\in \mathrm {BV}(\Omega ;{\mathbb R}^N)\) with \(Du\ll \mu \). The positive Radon measure \(\mu \) is only assumed to satisfy \(\mathcal L^n\ll \mu \).
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Acknowledgments
This research was done while P. L. was visiting the Oxford Centre for Nonlinear Partial Differential Equations (OxPDE) from September 2014 to July 2016. During this time, P.L. was supported by Aalto University as well as the Finnish Cultural Foundation.
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Communicated by L. Ambrosio.
