Lower semicontinuity for an integral functional in BV

Abstract

We prove a lower semicontinuity result for a functional of linear growth initially defined by \[ \int_ΩF\left(\frac{dDu}{dμ}\right)\,dμ\] for $u\in BV(\Omega ;{\mathbb{R}}^N)$ with $Du\ll \mu$. The positive Radon measure $\mu$ is only assumed to satisfy ${\mathcal{L}}^n\ll \mu$.

References in corpus (1)

• On Rank-One Convex Functions that are homogeneous of Degree One